GWEN IFILL: Pope Francis, Chinese President Xi, and John Boehner - three leaders making big news, all within 24 hours.

We explore the impact tonight on Washington Week.

HOUSE SPEAKER JOHN BOEHNER (R-OH): (From video.)

It's been an honor to serve in this institution.

GWEN IFILL: One day after the triumph of hosting the pope at the Capitol, the House Speaker takes Washington by surprise, announcing he'll quit next month.

What it means for politics and policy.

Meanwhile, Pope Francis takes the U.S. by storm, chiding Congress gently.

POPE FRANCIS: (From video.)

Legislative activity is always based on care for the people.

GWEN IFILL: Embracing children and the poor, and making the moral case for refugee relief, against the death penalty, and on behalf of climate action.

POPE FRANCIS: (From video.)

God bless America.

(Cheers, applause.)

GWEN IFILL: While at the White House, superpowers agreed to cooperate on some things while waiting each other out on others.

PRESIDENT BARACK OBAMA: (From video.)

That's part of the deal of being on the world stage when you're a big country, is you've got more to do.

My gray hair testifies to that.

GWEN IFILL: And on the campaign trail, Walker drops out, Rubio and Fiorina rise, and Trump and Carson stir the pot.

DR. BEN CARSON: (From video.)

I would not advocate that we put a Muslim in charge of this nation.

GWEN IFILL: Plus, Clinton finally makes a decision on the Keystone Pipeline.

FORMER SECRETARY OF STATE HILLARY CLINTON: (From video.)

I oppose it.

GWEN IFILL: Covering the week, Dan Balz, chief correspondent for The Washington Post; Tom Gjelten, religion correspondent for NPR; John Harwood, chief Washington correspondent for CNBC; and Alexis Simendinger, White House correspondent for RealClearPolitics.

ANNOUNCER: Award-winning reporting and analysis.

Covering history as it happens.

Live from our nation's capital, this is Washington Week with Gwen Ifill.

Once again, live from Washington, moderator Gwen Ifill.

GWEN IFILL: Good evening.

Some weeks are so big that it takes the whole table to discuss it.

Tonight will be one of those nights, beginning with the precipitous political fall of House Speaker John Boehner.

Yesterday he met the pope.

Then he went home, told his wife he might quit today, woke up, went to Starbucks, Pete's Diner, and then he went to Capitol Hill to tell his staff, today's the day.

SPEAKER JOHN BOEHNER: (From video.)

This turmoil that's been churning now for a couple of months is not good for the members and it's not good for the institution.

My first job as speaker is to protect the institution.

GWEN IFILL: What the speaker was hinting at there was that the institution he is in charge of, especially the House Republican Caucus, is in peril.

And Boehner himself was increasingly the target.

Check out what happened today at a meeting of conservative activists in Washington when presidential candidate Marco Rubio broke the speaker's news.

SENATOR MARCO RUBIO (R-FL): (From video.)

Just a few minutes ago, Speaker Boehner announced that he will be resigning.

(Cheers, applause.)

GWEN IFILL: That reaction only scratches the surface of what happened here, John.

What did happen here?

JOHN HARWOOD: Well, I think we reached a moment in the House which is sort of a bookend with what's going on on the presidential campaign with Donald Trump and some of his supporters, which is that you've got a group of people within the Republican Party who are upset because they have not seen economic gains, they're concerned, fearful about the way the country's changing demographically, culturally.

And they want things that the political system and the Republican leadership in Washington cannot deliver.

John Boehner felt that crush of pressure.

Ever since he became the speaker and they won the majority, he had members pressing him to confront President Obama, confront the Democrats, pull off things that were beyond the power of the Republican majority in the House to do.

The new version of that fight came in the question of do we shut the government?

Can we defund Planned Parenthood?

Are we going to raise the debt limit?

All those things coming together this fall.

And the dissidents were pressing on John Boehner, looking at him as somebody who was potentially going to sell them out again.

And so he stepped aside and said, as we heard in that clip, for the good of the institution I'll step aside.

Now, it's only for the good of the institution for a short period of time.

They will get past this moment.

They still have to resolve the disconnect between what those members want and what is possible to achieve.

GWEN IFILL: Well, let's talk about the disconnect because, Dan, you actually wrote about this today.

First of all, did he jump or was he pushed?

Is it a distinction without a difference?

And does this mean that this party can govern?

DAN BALZ: I think it is a basic question.

You know, we - you look back at 2010 when they had a big victory after losing elections in 2006 and 2008, and it looked like a party on the rebound.

And in fact, what we've seen since then is this is a party in great disarray, with warring factions constantly at one another's throats, tensions that we've seen play out repeatedly in the House.

And as John said, we're now seeing those same kinds of tensions play out in the presidential race.

One of the things that they have never quite been able to square is in Washington, in particular, how do you govern in this environment?

The agenda of the tea party movement in particular, and a lot of the younger members who came in in that period, is to stop government, not to keep government moving.

And this creates real dissonance within the Republican conference.

GWEN IFILL: And it makes Democrats incredibly happy.

Let's hear what the President had to say today about it when he was asked during his press conference in the Rose Garden.

PRESIDENT BARACK OBAMA: (From video.)

The one thing I will say is that my hope is there's a recognition on the part of the next speaker, something I think John understood even though at times it was challenging to bring his caucus along, that we can have significant differences on issues, but that doesn't mean you shut down the government.

GWEN IFILL: Now, this has been a refrain for Democrats all week, Alexis, which is: They're going to shut down the government because, of course, this makes them very happy, because it didn't work out well last time for Republicans.

ALEXIS SIMENDINGER: And the president was, you know, offering this idea that perhaps John Boehner's, you know, caucus has learned some lessons.

And, you know, that was the words we heard in the Rose Garden.

That was not the demeanor of the president.

In fact, allies of the president in the White House were pretty quick to say that they're not expecting anything to change more favorably, from the White House perspective, no matter who it is who's speaker, for all the reasons that we just heard John and Dan describe.

The president has moved on.

And we can argue, you know, what these two men meant to each other or didn't mean to each other, but the one thing that is very much the case is that John Boehner and the weaknesses or vulnerabilities that he had changed the way the president governed in the second term.

He had to figure out ways to go around Congress and push his agenda, although he had to give up.

He had to give up immigration reform, gun control, the aspirations for climate change, even.

So much has changed for these two in ways that were unsatisfactory to both of them.

GWEN IFILL: We're going to get to more about the pope, but it seemed that one thing we saw for sure about John Boehner this week, Tom, is that this was a big moment for him, being able to get the pope to come to Capitol Hill and maybe, I don't know, something about that moment focused his mind.

TOM GJELTEN: Well, he told a reporter for Dan's newspaper, right, that this was something he'd been working for for 20 years, and now that he's accomplished it, you know, that that was the big triumph that he'd been waiting for.

I mean, as we've mentioned, there are certainly these other political factors that entered in, but that was a very emotional encounter for John Boehner.

GWEN IFILL: Or, as he said, me, emotional?

(Laughter.)

TOM GJELTEN: Yeah, it doesn't take too much.

JOHN HARWOOD (?

): You might call it a come to Jesus moment.

GWEN IFILL: Yeah.

JOHN HARWOOD: Gwen, I will say one thing.

I do think the short term is not irrelevant here.

I talked to a Republican member this afternoon who said, John Boehner's got five weeks left.

He has become martyred in this cause.

He's going to be able to do, and be willing to do, things he wouldn't do if his job were still on the line.

So there's a possibility we could get a long-term spending deal - long-term meaning through the 2016 election - a long-term debt limit increase, highway bill, reauthorization of the Ex-Im Bank - all that's possible.

GWEN IFILL: And also a leadership fight somewhere between now and then.

Thank you, everybody.

Only yesterday Pope Francis was suggesting that our nation's leaders observe the golden rule, do unto others as you would have them do unto you - leadership race.

In this case, the pontiff was talking about the treatment of Syrian refugees, but as he traveled from Cuba to Washington to New York City this week, he managed to touch nearly every political and moral third rail - from abortion, to marriage, to climate change, to immigration - while arguing that he is neither right nor left.

POPE FRANCIS: (From video.)

There is another temptation which we must especially guard against.

The simplistic reductionism which sees only good or evil or, if you will, the righteous and sinners.

GWEN IFILL: The pontiff was embraced by everyone he encountered, especially here in Washington, the very land of simplistic reductionism.

(Laughter.)

Tom, how did the pope walk that third rail?

TOM GJELTEN: Well, Gwen, just listen to that voice.

It's such a gentle voice.

He projects such humility.

And I think it's - and people feel like it's a genuine humility.

You mentioned he's talking about the golden rule in the context of Syrian refugees.

Well, there's not a big push to bring in a lot of Syrian refugees, and yet that line got more applause than any other line in his speech.

GWEN IFILL: My theory is they understood him.

They were struggling with his accent.

TOM GJELTEN: Well, I think some of them had text.

But there something about the simplicity of the golden rule and the way he said it that I - if anyone else had said it, it would have sounded like empty words.

But somehow when he says it, you actually think about what he's saying and you kind of take it to heart.

I think that has been a big part of his appeal.

GWEN IFILL: What did he come to America to do?

TOM GJELTEN: He came - you know, if you look at every speech he gave, beginning with the White House, he says, I am the son of an immigrant.

He goes to Congress and the first thing he says: I too am a son of this continent.

I think he really wanted to get people to think in a much more inclusive way about who are Americans, not just the people that settled on the East Coast, but people who settled in California and people even in Argentina.

I think he really wanted to expand our notion of humanity and who should be part of this country.

GWEN IFILL: Alexis, I'm always curious in these cases whether everyone he encounters is not - it's harsh to say that they're using him, but they are using him for their own purposes.

So if he's standing next to the president, the president says I agree with him.

If he's standing next to the speaker of the House, he says I agree with him.

Is that what we saw a little bit, or am I being a little too harsh?

ALEXIS SIMENDINGER: Well, I would say that Pope Francis has a real knack for use of symbolism and communication that maybe some folks in Washington admire.

But you're absolutely right, watching President Obama with the pope in the greeting, it was clear President Obama enjoys this pope, who he had met before, leans into him physically and, of course, was so heartened to hear words that - especially about climate change - upon which they agree, or immigration, upon which they agree.

And the use of the pope is, you know, that universal embrace of hearing what you want to hear, but also trying to I think emulate his communication skill and utilize that - the moral - the moral frame in which he put the president's own political agenda.

TOM GJELTEN: But you know, Gwen, he's a master at uniting what seemed to be contrary ideas from the left and the right.

He would talk about - he'd make an allusion to abortion and immediately follow it with a comment about the death penalty.

He would talk about the family - GWEN IFILL: Yes, which is consistent, when you think about it.

TOM GJELTEN: Well, of course it is.

And it's been a consistent part of Catholic doctrine for a long time.

But he'd talk about the family being under threat in a way that made you think he's talking about same sex marriage, and then he would go to the family being threatened by income inequality.

So you never really knew where he was going to go.

He would bring these issues together in a very artful way.

GWEN IFILL: Dan, how does what he had to say about immigration in particular, we are all immigrants, that kind of argument, how does that reverberate in this particular political environment we're in?

DAN BALZ: Well, it strengthens the hand of the people who say we need to have comprehensive immigration and we need to lower the temperature of the debate over this.

I mean, the contrast between the way he speaks about these issues - put aside where he stands on them - the way he speaks about these issues versus the way Donald Trump speaks about these issues is night and day.

And one of the - I thought one of the most interesting things he said was when he spoke to the bishops here in Washington on Wednesday, just after he had been at the White House.

And one of the things he was saying to them was, you have to be pastors and you have to speak to people in a certain way.

Harsh language is never the right way to do it.

And so he's able, as Tom said, to talk about very controversial issues.

And he has a controversial agenda, but he's able to do it because he speaks without harshness.

GWEN IFILL: And he's also able to soften a little bit his tone.

In other parts of the world, he's been a lot tougher than he was here about exactly the same issues, especially about capitalism.

We've got to move on.

As we sit here tonight, people far fancier than we are are over at the White House attending a state dinner for Chinese President Xi Jinping.

It is surely a lovely evening, but no formal toast can overshadow the unresolved issues between the two superpowers.

For instances, Presidents Obama and Xi agreed to reduce emissions and slow climate change.

But when it came to cybertheft, which has stirred great East-West suspicion, the promises were considerably more vague.

PRESIDENT BARACK OBAMA: (From video.)

We have jointly affirmed the principle that governments don't engage in cyberespionage for commercial gain against companies.

That all, I consider to be progress.

The question now is, are words followed by actions?

GWEN IFILL: But that was not the only open-ended question today, Alexis, was it?

ALEXIS SIMENDINGER: No.

And it was interesting, because, you know, what did President Xi get out of this?

He really got the full panoply of the United States giving him this 21-gun salute and the state visit and all that, which is very important to him and his country.

What did the president get out of it?

The president had - you know, was really heralding something that they talked very little about today, but we've talked a lot about this week, and that is climate change - that China as the largest emitter of greenhouse gases came together with the United States in a way that will bolster both countries when they go later on this year to the U.N. climate summit.

The president has not been able to achieve the kind of embrace of something that they've agreed on.

China's agreed to do a cap and trade, you know, policy in China, which they've been working on in pilot program for a year.

Trading, bartering - JOHN HARWOOD: Can that pass the Senate in China?

(Laughter.)

ALEXIS SIMENDINGER: And you know, very interesting because the president could not get this through here in the United States.

But together, the idea that China and the president's talking about trying to encourage India to think in the same way, the president will be meeting the - Modi in the United Nations this weekend.

So what was interesting was they didn't really come to any kind of agreement on cyber.

Keep in mind, when the president goes to New York this weekend for the U.N. he will be staying at a different hotel.

Why?

GWEN IFILL: Because they think they're being spied on at the Waldorf-Astoria.

ALEXIS SIMENDINGER: Because the Chinese bought the hotel he used to stay at, the Waldorf-Astoria.

So the president's talking about one narrow element.

And they disagreed also on the South China Sea, in a very, I would say, assertive way today, because the Chinese president basically said stay out of this.

This is an ancient territorial recognition that this is Chinese water.

GWEN IFILL: And John, this - DAN BALZ (?

): And that's very risky issue.

GWEN IFILL: That's a very risky - and John, the other - the other thing that is kind of - cast a shadow over this visit was the Chinese stock market has really been taking a hit.

There's been real concerns about the Chinese economy.

Were they - did they allude to that at all today, or did they just agree not to talk about it?

JOHN HARWOOD: Well, I think that wasn't the focal point of the visit, but it's the backdrop of the visit, because weakness in China - it's really interesting.

You know, on the presidential campaign trail, Donald Trump talks about China eating our lunch economically.

In fact, we want the Chinese economy to be doing better than it is, because when the Chinese economy slows down the world economy slows down.

So there's an interesting balance of interests there, where the United States wants China to trade with us in a fair way, we want them to rebalance their economy, build up the consumer part of their economy, not so much emphasis on exports at the expense of American manufacturers.

But we do want China to be doing better.

And nobody's quite sure how much to trust the assessments from the Chinese government of how well the economy's doing.

GWEN IFILL: Tom, you spent some time in China on a fellowship earlier this year.

And I wonder how important do these meetings seem to the Chinese, or is it very, very distant?

TOM GJELTEN: I think - well, Alexis alluded to this.

I think the Chinese people and Chinese leaders really want their country to be recognized as being on the same par as the United States and any other great power.

So those - from that point of view, I think they are really important.

There's an incredible sensitivity in China to issues of sovereignty and nationalism.

And you know, the South China Sea - we think of the - we think of Chinese assertiveness in the South China Sea as being really aggressive.

That's an issue that draws tremendous support, popularity in China because, you know, they feel - it's very important to understand the Chinese people feel they once had - once were recognized as having a great civilization.

They've really been mistreated for the last hundred years.

Now they're very eager to get back on the front lines again.

GWEN IFILL: And, Dan, I wonder, as we watch this Obama-Xi relationship, whether we're beginning to look at all of these bilateral relationships in terms of the president's legacy and whether there is one there.

DAN BALZ: Well, I think everything that he does over the last 14 or 15 months of his presidency is going to be put in that box and examined in those ways.

You know, history tells us that it's very hard to judge in the moment, but I think in his relations with Congress, his relations with the Russians, his relations with the Chinese, and everything else we will be looking at as a possible piece of his legacy.

GWEN IFILL: And, of course, that's exactly the interpretation they resist at the White House.

ALEXIS SIMENDINGER: Oh, absolutely.

Yes, exactly.

GWEN IFILL: We can't resist anyway.

ALEXIS SIMENDINGER: Yes, absolutely.

GWEN IFILL: And we have reached the point in the 2016 contest where elbows are landing.

Marco Rubio is beginning to push back against Donald Trump.

Trump is pushing back, once again, against Fox News, and against his competitors.

DONALD TRUMP: (From video.)

You have this clown, Marco Rubio.

I've been so nice to him.

(Boos.)

I've been so nice.

(Boos.)

I've been so nice.

And then - no - but he's in favor of immigration and he has been.

He has been.

It was the Gang of Eight.

And you remember the Gang of Eight, it was terrible.

(Applause.)

And then he went down in the polls.

GWEN IFILL: And Wisconsin Governor Scott Walker has dropped out entirely, but not without a final call to clear the field.

WISCONSIN GOVERNOR SCOTT WALKER (R): (From video.)

I encourage other Republican presidential candidates to consider doing the same so that the voters can focus on a limited number of candidates who can offer a positive conservative alternative to the current front-runner.

GWEN IFILL: So far, no takers.

(Laughs, laughter.)

So, Dan, what really happened with Scott Walker?

Why did he really drop out?

DAN BALZ: Well, two things.

One is he was - he was not quite prepared for the campaign.

He got a big burst of attention because he gave a very strong speech in Iowa early in the year to a group of conservatives, and it kind of rocketed him to the top tier of the race I think before he was ready for it.

And since then he's made a number of mistakes on his own.

He has changed his position on some issues.

He's misstated things.

He's had to backtrack on some things.

So there was a question about, was he ready?

The second is he was totally overshadowed by Donald Trump.

I mean, when Donald Trump got into this race, Walker was the leader in Iowa.

And since then he's gone down dramatically.

And in this environment, which is a very tough environment for candidates because of the competition for money, if your poll numbers go down the money dries up.

And that's what he found.

He had a deficit of $700,000 in his campaign.

He had a budget that was going to cost a million a month and no prospect that he was going to be able to raise it.

And so he pulled the plug.

GWEN IFILL: And who benefits from the plug being pulled, one less person being in this race?

DAN BALZ: It's hard to say.

I think Rubio will benefit in some ways.

Jeb Bush has picked off some of his people.

The truth is, by the time he got out he did not have that much support in terms of voters.

Some of his donors - everybody's going after some of his super PAC donors.

But that's going to be spread around.

GWEN IFILL: You had an interview this week, John, with Jeb Bush.

Does he look like he's poised to jump in, or is - you know, Scott Walker was once the front-runner, Jeb Bush was once the front-runner; everything's different.

JOHN HARWOOD: I got no sense from Jeb Bush that he's ready to get out of the race at Scott Walker's invitation.

(Laughter.)

And if you've got $100 million in your super PAC - GWEN IFILL: You don't think that Scott Walker was really talking to Jeb.

JOHN HARWOOD: No.

GWEN IFILL: No.

JOHN HARWOOD: But there's a reason to stay around and a reason to expect that Jeb will be around for quite a long time.

He was - continued to be annoyed by the needling from Donald Trump.

We talked about his paleo diet.

He's lost 30 pounds.

I said, well, maybe that makes you low energy.

And he said, no, I'm high energy and I campaign.

I don't just ride down the escalator and have a press conference.

I'm out pounding the pavement.

GWEN IFILL: Jeb Bush gave an interview in which he said that - he was asked by someone - a South Carolina voter how he's going to win the black vote, and his response was, well, I'm not going to give them free stuff.

What was that?

JOHN HARWOOD: You know, that's - it's an echo of what he did in 1994, when he got a question and they said, what are you going to do for blacks in Florida, and he said, probably nothing.

And that was his way of saying I'm not approaching this from an identity politics standpoint, I'm not approaching this for, you know, race-specific benefits.

And he was echoing a little bit what Mitt Romney was saying in 2012 and trying to signal people that I'm not somebody who's going to be loose with government purse strings.

GWEN IFILL: I want to talk to you about Democrats before we run out of time, because we of course saw Hillary Clinton come out and finally talk about the Keystone Pipeline.

She's against it, even though she seemed to signal differently when she was secretary of State.

And Bernie Sanders is once and forever really, really ahead in New Hampshire.

DAN BALZ: He is.

Every poll we see now out of New Hampshire shows Bernie Sanders in the lead, and he's crept up in Iowa as well.

And in some national polls he's crept up, although she's still got a pretty good lead in almost all the national polls.

But there's no question that he's a - he's a force in New Hampshire, and the Clinton campaign recognizes that.

And I think there's - there is and will continue to be a debate within the campaign of how you - how you confront that, when you confront that.

I think everybody's anticipating that the debate in Las Vegas in mid-October will be the moment at which this could happen.

And then you've got, of course, Vice President Biden kind of lurking on the sidelines.

Maybe he's going to get in, maybe he's not.

Nobody can quite tell where his head is on that.

But that's another factor that's roiling the Democratic race.

GWEN IFILL: There is so much going on that we can't get to all of it, and it breaks my heart.

But we have to go.

And, as always, the conversation will continue online, we promise, on the Washington Week Webcast Extra where, among other things, we'll preview the president's meeting next week with Russian President Putin.

You can find it later tonight and all week long at PBS.org/WashingtonWeek.

Before we go tonight, we want to introduce you to the newest member of the Washington Week family, River Jude Brickey, who makes our production manager, Tim Dombro, a proud granddad.

Congrats, as well, to River's parents, Julian and Layla (sp).

Keep up with developments with Judy Woodruff and me on the PBS NewsHour, and we'll see you here next week on Washington Week.

Good night.