PETE WILLIAMS: Mr. Trump goes to Washington, agreeing with House Speaker Paul Ryan it's time to unite the Republican Party.

Hillary Clinton can't stop her campaign on two fronts, against Trump and Bernie Sanders.

Plus, the White House steps into the highly charged debate over schools and transgender rights.

I'm Pete Williams, in for Gwen Ifill, tonight on Washington Week.

HOUSE SPEAKER PAUL RYAN (R-WI): (From video.)

We had a very encouraging meeting.

It's very important that we don't fake unifying, we don't pretend unification, that we truly and actually unify so that we are full strength in the fall.

DONALD TRUMP: (From video.)

Well, I think we really had a great meeting today, and I think we agree in a lot of things.

And it'll be a little process, but it'll come along.

PETE WILLIAMS: Donald Trump turns on the charm, hoping to win over reluctant rank-and-file Republicans leery of his unpredictable campaign.

DONALD TRUMP: (From video.)

Donald J. Trump is calling for a total and complete shutdown of Muslims entering the United States.

DONALD TRUMP: (From video.)

It's a temporary ban.

It hasn't been called for yet.

Nobody's done it.

This is just a suggestion.

PETE WILLIAMS: Can the GOP be at war with its presumptive nominee ahead of what's sure to be a contentious general election campaign?

SENATOR BERNIE SANDERS (I-VT): (From video.)

Let me be as clear as I can be: We are in this campaign to win the Democratic nomination.

(Cheers, applause.)

PETE WILLIAMS: The big 15-point Sanders win in West Virginia this week did little to distract Hillary Clinton from her new focus, Donald Trump's refusal to release his tax returns.

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

My husband and I have released 33 years of tax returns.

We got eight years on our website right now.

So you got to ask yourself, why doesn't he want to release 'em?

PETE WILLIAMS: Plus, the Obama administration tells public schools allow transgender students to use the bathrooms that match their chosen gender identity, with federal funding at stake.

We examine that politically charged debate and the race for the White House with Susan Davis, congressional reporter for NPR; Abby Phillip, political reporter for The Washington Post; Jeanne Cummings, political editor for The Wall Street Journal; and Josh Gerstein, senior White House reporter for POLITICO.

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, sitting in for Gwen Ifill this week, Pete Williams of NBC News.

PETE WILLIAMS: Good evening.

Anyone who happened to be near the U.S. Capitol Thursday could be forgiven for thinking the pope was back in town.

Nearly every available news camera in Washington was focused on the front door of the Republican National Committee for a meeting between Donald Trump and Paul Ryan.

When it was over, both of them accentuated the positive.

DONALD TRUMP: (From video.)

I thought it was really a very, very good meeting.

I think Paul felt the same way, and everybody else did also.

I think he's doing a good job.

HOUSE SPEAKER PAUL RYAN (R-WI): (From video.)

I do believe that we are now planting the seeds to get ourselves unified, to bridge the gaps and differences.

And so, from here, we're going to go deeper into the policy areas to see where that common ground is and how we can make sure that we are operating off these same core principles.

PETE WILLIAMS: So, Susan, who needed this meeting more, Trump or Ryan?

SUSAN DAVIS: Well, it's a little bit of both.

And we should say that part of what caused this meeting is House Speaker Paul Ryan has so far declined to formally endorse Donald Trump, unlike his counterpart in the Senate, Senate Majority Leader Mitch McConnell.

You know, Paul Ryan is speaker of the House, and he has a majority to protect.

And there's a lot of Republicans who are concerned about Trump's effect at the top of the ticket, particularly in the competitive races that decide the majority.

So, in some ways, you know - and the fact that Donald Trump has brought all these new voters into the party, Paul Ryan wants to protect his majority and not alienate these Trump voters.

But then, on the other side of this equation, you have people that we'll call Ryan Republicans, these more traditional conservative Republicans, who are looking at Donald Trump and are not ready to get behind this guy.

But these are the same Republicans that, if Donald Trump's going to have a chance at winning the White House, he's going to have to win over these kind of Republicans.

And most recent polls have showed up to 25 percent - about a quarter of people who identify as Republican voters say they're not ready to vote for Donald Trump.

PETE WILLIAMS: Well, they talked, Jeanne, about unity.

What does unity in the Republican Party mean - they just stop criticizing each other, or they actually agree on things?

JEANNE CUMMINGS: Well, it's probably going to be a combination of both.

But I do think they're going to try to move Trump, which is dangerous for him.

But within 24 hours or less, he was moving on the Muslim ban.

And as we all recall, when Donald Trump said that, Paul Ryan was one of the first to grab a microphone and rebut and refute what the Republican Party standing is on those kinds of issues.

So we probably will see some movement.

And what we could also see, though, is that they're going to have to give Trump something, too.

And it's not unusual to have a unified Republican Party where the two candidates at the top have had their own disagreements.

Certainly, Paul Ryan and Mitt Romney were not on the same page on a lot of policy.

So Hillary Clinton in many ways will become a unifying force for the Republicans, but they do need to settle some of their bigger disagreements before they get there.

PETE WILLIAMS: But I thought part of Donald Trump's whole pitch was, hey, look how well I did with the way I was; why should I change that now?

JEANNE CUMMINGS: Because what - he can't win with what he had.

He can't win a general.

He could win the primary.

But now he's got to expand that coalition to these voters that are uncertain about him.

He can't - a Republican can't win the presidency without winning some of the suburbs.

You can have Hillary Clinton go in and win Philadelphia, but then the Republican has got to go to the doughnut and start countering in those areas.

Well, in those areas some of the most influential voters are women.

And if you look at polls, he is in terrible shape when it comes to women, particularly suburban women.

ABBY PHILLIP: Donald Trump has to add to the Republican coalition, not take away from it.

So he really has to really work on the Republican base.

I was talking to Republicans in swing states over this past week, and they were saying, you know, he could actually put together something that works in, you know, the Midwest if he solidifies the Republican base.

These are Republican voters who are actually pretty traditional.

They are actually tied to the establishment.

They want to see the Republican Party espousing certain principles and following through on them and being fairly consistent.

These are people who like Paul Ryan, for example.

And so that's one of the reasons why they kind of need to come together and actually agree on some things, because I think Donald Trump needs Paul Ryan.

He's a pretty popular Republican figure in a world in which most Americans don't really like Congress very much.

And I think he's going to need to get those people who like Paul Ryan and who Paul Ryan can get out to vote to be out there for him.

PETE WILLIAMS: So, Susan, if it's correct that you're not going to get Paul Ryan unless his members are with him, I heard some of the Republican members say that one reason they're reluctant to go for Donald Trump is they don't know who - you know, they're going to get up every morning while they're running for reelection and have to respond to his latest tweet.

SUSAN DAVIS: I've talked to members who say that, too, that part of - and you know, there hasn't been a huge cascade of endorsements of Donald Trump, although he did secure a lot more this week.

Nine committee chairmen have come out this week to support him, unlike the speaker.

But part of that is what they say, is what he says today might be different than what he says tomorrow, might be different than what he says two months from now.

So why not hold back your endorsement in case he says something that might hurt you in your own race?

There's a lot of hesitance.

But I would also say that every Republican, to the person, that I've talked to this week on Capitol Hill believes that Paul Ryan is going to endorse Donald Trump before the convention.

JEANNE CUMMINGS: And Trump can cut both ways, especially in congressional races.

SUSAN DAVIS: Yes.

JEANNE CUMMINGS: Because there are Democrats who are sitting in rural or semi-rural districts that are really very scared about how he might activate voters on Election Day.

Louise Slaughter in Upstate New York had a very close reelection in the last cycle, won by a tiny, tiny margin.

She has the same opponent, so it's a quality opponent.

Donald Trump went in her backyard, and there we are, 10,000 people.

Now, they may be regular voters, they may not.

There's a lot of debate about whether he is truly bringing in new people or is he converting general election voters to vote in the primary.

So lots of work to be done on that.

But at any rate, I think there are as many Democrats worried about Donald Trump as there are Republicans.

PETE WILLIAMS: Let me ask you another question about money.

Is part of Donald Trump's overture to the Republican Party because now in the general he needs their money, he's not going to pay for it himself?

JEANNE CUMMINGS: Absolutely.

I mean, it costs almost a billion dollars to run a presidential campaign.

He can't do it.

He'd have to be selling buildings, because he's not liquid in that fashion.

So he does need the Republican Party.

At first he said the party will finance my general election.

They can't.

He clearly didn't understand about campaign caps and limits on donations.

He's got to have it all.

He's got to have all of those financial tools to his disposal.

And so, as we reported this week, his super PAC is holding their first event.

They've got it scheduled.

He's got his own campaign fundraiser already scheduled.

And the thing for him where this is going to hurt is a big part of his platform and his attacks was he called his rivals "puppets" because they were beholden to wealthy donors.

Well.

(Laughter.)

PETE WILLIAMS: Abby, who better represents Republican voters, Paul Ryan or Donald Trump?

ABBY PHILLIP: It's really hard to know at this point.

I mean, the Republican Party is very much split.

I mean, I think Paul Ryan probably has a good 25 to 30 percent of the Republican Party.

They need all of them.

And Donald Trump has on his side about 25 to 30 percent of the Republican Party.

They need all of those people in order to win.

And the other thing about the fundraising, as Jeanne was saying, was that Republicans are facing a situation in which the Democratic candidate, the likely nominee, has been raising money with the DNC for six months, essentially.

Just this week, she held two fundraisers where it cost about $100,000 a head to walk into the room.

I mean, this is all money that is earmarked for the general election.

They have a lot of catching up to do.

In order to do that, Donald Trump needs to make nice with his party very, very quickly.

PETE WILLIAMS: Well, whose party is it?

Who's in charge of the Republican Party?

SUSAN DAVIS: Donald Trump is in charge of the Republican Party.

JEANNE CUMMINGS: Yeah, I would agree with that.

SUSAN DAVIS: I mean, he won the primary.

The nominee sets the tone.

And as he said - he had this really interesting line where he said it's called the Republican Party, it's not called the Conservative Party.

And his point is his positions that go against this Paul Ryan orthodoxy on taxes, on trade, on Medicare, have won him the nomination, and that this sort of populist wave that has come into the party is driven by Donald Trump, and he is changing what it means to be a Republican.

JEANNE CUMMINGS: Well, and that's one of the reasons that the stop Trump people say the only way they get their party back is if he loses - if he loses in November.

If he wins, what we're seeing is the start of a transition from a conservative Republican Party to a populist Republican Party - very different creatures.

PETE WILLIAMS: Well, there is still a primary going on out there, and any thought that Bernie Sanders might shift his campaign into neutral vanished after his big win this week in West Virginia.

He says he's still in it to win it, while Hillary Clinton tries to look over his head toward the general election.

SENATOR BERNIE SANDERS (I-VT): (From video.)

I want you all to know that this campaign will fight for every remaining vote and every remaining state.

HILLARY CLINTON: (From video.)

If I'm so fortunate enough as to be the nominee, I am looking forward to debating Donald Trump come the fall.

(Cheers, applause.)

PETE WILLIAMS: Abby, you've written that Hillary Clinton is putting more energy into industrial states that have traditionally gone for Democrats.

Why is that?

ABBY PHILLIP: It's all about the populism.

It's about the economy and it's about really the sentiment that people feel like they don't like politics as usual.

And Donald Trump is nothing if not an unconventional candidate.

I mean, I think the Clinton campaign feels very much like this is territory that they know how to run in.

The problem is, they don't actually know what Donald Trump is going to do.

And there are rural parts of the state where in the primary he did quite well.

That, you know, gives them a little cause for concern.

If he can bring out people that they've really never seen before in general elections, then Democrats are going to have to do a sort of counterbalancing in the suburbs, bringing out a lot more women, bringing out a lot more minorities, in states where there are - it's a very white population overall.

That's a place where Donald Trump can do pretty well.

And so there is - there's a certain amount of concern.

I think Democrats on the ground in particular are concerned because they see the economy as a real uncertainty, that Hillary Clinton hasn't quite landed on exactly the right message that she needs to compete there.

JOSH GERSTEIN: Abby, I wonder, what do Clinton's people say about what has changed since 2008?

You know, she did so well in some of these places up against Barack Obama - in West Virginia, for example, and a lot of the other - a lot of the Rust Belt industrial states - and she's done so poorly in the face of this Sanders onslaught.

Do they think they can recover that eight-year-old momentum?

ABBY PHILLIP: I don't think they - I actually don't think they think that they can recover it, because I think they recognize that some of the support that she got in places where Obama didn't do well was a sort of anti-Obama vote.

There's no anti-Obama vote now.

There's a Sanders vote, and he's actually in some ways speaking to what voters want to hear in terms of the strictly populist economic message.

It's just a very hard thing for her to crystalize because Hillary Clinton wants to talk about the government.

She wants to talk about programs.

She wants to talk about what she's done.

And voters are saying, you guys are all terrible, we want to upend this whole system.

JEANNE CUMMINGS: Well, the other thing that's gone on is that the Democratic Party in the last eight years has changed.

Just as Republicans are facing change - a little more traumatic - the Democrats took some time, but this party right now - the party base - is more liberal than the president, and certainly more liberal than Hillary Clinton when she set foot on the stage for this election.

And if Bernie Sanders has done anything to Hillary Clinton, he has moved her to the left on some issues.

And people at first thought, oh, this is going to be awful, but in fact it actually puts her more aligned with her own party because the party has changed so much.

PETE WILLIAMS: Well, what about those Sanders voters, though?

I mean, are they going to be with her in the general election, or will they sit at home?

JEANNE CUMMINGS: Well, I think that a lot depends on Bernie Sanders.

My guess is he does the work that is necessary to try to keep them involved.

The Clinton campaign is sincere when they say we're not going to stop Bernie, we don't want him to quit; the only way we can - or the quickest way we can bring this all together - PETE WILLIAMS: They still don't - even now they don't want him to quit?

JEANNE CUMMINGS: Right, because here's the point.

If you're thinking ahead to how do we unify, then the way you do that is you let all those Sanders people in California, New Jersey, wherever, cast their vote.

Let them vote for him, and then bring it together.

And so, yes, they want to get to the end of this.

And Bernie is just - is more animated about beating Trump.

And if he, you know, works with Clinton's campaign and takes that message to his people, then I think that a good number of them are going to stick with her.

PETE WILLIAMS: So let me ask all of you, there was some interesting polling this week about a potential Clinton-Trump matchup.

What did we learn from that?

SUSAN DAVIS: It was battleground state polling in Florida, Ohio, and Pennsylvania - probably the holy trinity of battleground states.

And it showed Clinton and Donald Trump neck and neck, that it looks very competitive.

The two subsets of data in that that are really interesting is the polarization that we have in this country.

The gender gap, where women are for Clinton and men are for Donald Trump, has never been wider.

And the racial gap - the white voters to nonwhite voters; white voters for Donald Trump, nonwhite for Hillary Clinton - is equally as wide.

And if those numbers hold, what it tells us is that this is going to be one of the most polarizing elections we've had, far more polarizing than the last two, and it's going to be a really ugly general election fight.

ABBY PHILLIP: And what is also interesting about the sort of white/nonwhite breakdown is that one of the criticisms of that poll was that the white breakdown was a little too high.

It didn't reflect what we are likely to see in November.

But it also reflects a possible scenario in which Donald Trump could ratchet up the turnout and participation of white voters in a way that would bring some of these races, in Ohio and in Pennsylvania in particular, much closer than Democrats would like.

That's a possibility.

When I talk to people who look at the numbers, they say we don't think it's going to work that way because it's actually really, really hard to do that, but it is possible.

And that's the possible scenario.

PETE WILLIAMS: All right.

Thank you.

One other thing besides politics, and that's a big story this week.

The Obama administration late this week sent a letter to all the nation's public schools and colleges telling them they must allow transgender students to use the bathrooms conforming to their gender identity.

Not to do so, the letter said, would amount to sex discrimination.

But some conservatives call this an attempt at blackmail.

WHITE HOUSE PRESS SECRETARY JOSH EARNEST: (From video.)

What the framework does provide is advice for how school administrators can protect the dignity and safety of every student under their charge.

And that advice includes practical, tangible, real-world suggestions to school administrators who have to deal with this issue.

TEXAS LIEUTENANT GOVERNOR DAN PATRICK (R): (From video.)

Our parents and parents all across America do not want their children showering together.

They don't want boys in the girls' rooms.

This is unheard of.

And this is the biggest issue, I think, for families and schools since prayer was taken out of public schools.

PETE WILLIAMS: This week began with the Justice Department suing North Carolina over its bathroom law and a passionate call for transgender rights from Attorney General Loretta Lynch.

ATTORNEY GENERAL LORETTA LYNCH: (From video.)

It was not so very long ago that states, including North Carolina, had other signs above restrooms, water fountains, and on public accommodations keeping people out based on a distinction without a difference.

PETE WILLIAMS: Josh, this was an unusual move by the administration.

What's behind it?

JOSH GERSTEIN: Well, it was a pretty dramatic move.

I mean, this is something the administration's been working on for some time.

I think it was accelerated by the fight going on in North Carolina about the law that they passed at a statewide level that essentially prohibited these types of rules that some places, some schools were starting to implement, prohibited these kinds of protections.

What was maybe most significant about what the administration did was it eliminated one of the accommodations that had been worked out in a lot of these districts where this transgender issue had come up, which was to set up private facilities for people that were transgender, where they could have privacy.

They said that's not good enough; you have to allow them to use the group facility of their choice, regardless of - you know, if that's their choice.

And so it was a pretty dramatic move, but then the rhetoric as well I thought was very, very strong, especially coming from, like, the nation's first African-American attorney general.

To have her compare it to the Jim Crow laws is about as strong as you can be.

PETE WILLIAMS: And in talking about North Carolina, of course, she's talking about her home state.

This sort of seemed like it came out of nowhere, though.

I mean, it's not - has it been something that's been a big push for the administration before?

JOSH GERSTEIN: It has not been a big push for the administration before.

But quietly, for the people that were interested in this, they had taken a series of steps in recent years in this direction.

What I think really escalated this may have been the battle last November in Houston.

There was a ballot measure that went in there where voters were allowed in a referendum to vote on an ordinance that people said would have allowed people to pick any bathroom they wanted to use.

PETE WILLIAMS: And it was voted down.

JOSH GERSTEIN: And it was voted down by a pretty substantial margin.

And that really energized and alerted people on both sides of this discussion that this is going to be a trench-fighting kind of battle.

And we saw this week that the Obama administration is prepared to weigh in that way.

JEANNE CUMMINGS: Josh, what's the nature of the letter that they sent out?

Is there some penalty?

Is it legally binding in any way?

I mean, Josh Earnest called it guidance.

Is that really all it is?

JOSH GERSTEIN: Well, it's a dear colleague letter - (laughter) - which sounds very, very innocuous.

But the threat that lurks behind it, right, is that federal funding could be cut off to any school district that doesn't go along with these rules.

But the question of whether it's legally binding is one that the courts are still working through.

The Fourth Circuit, which is based in Richmond, dealing with a case out of Virginia said that this kind of guidance from the Education Department is binding.

It's not clear that every other court would agree, and that was a 2-1 split decision.

And it really left for another day the question of whether this is binding in other places, in all kinds of state facilities, and also the question, frankly, of locker rooms and so forth, which can be a trickier issue than bathrooms.

SUSAN DAVIS: Josh, what do you think is driving President Obama's evolution on LGBT rights?

I mean, this is a - candidate Obama opposed gay marriage.

President Obama's come around on gay marriage.

And on this issue, they seem to be leading it not just, you know, responding to it.

JOSH GERSTEIN: Right.

It seems like the evolution - we've moved out of the evolution phase and into a much more accelerated phase.

I think part of it is that there's not a lot of time left on the clock for the Obama administration.

Some of these things are going to have to be fought out in court.

And if they're going to do that, we're already in May and they have to get this stuff moving by January.

It seems like, I'd have to say, they're probably likely to lose some of these battles in the trial courts, looking at the judges who've picked up these cases.

So there's going to be a time period here where they try to get an appeals court decision, another one in their favor, and maybe go to the Supreme Court.

PETE WILLIAMS: Very quickly, are there a lot of cases out there in the courts on this?

JOSH GERSTEIN: Well, in the past - in past years there aren't a lot supporting the Obama administration's position.

But now we have about four or five cases, many of them revolving around this North Carolina law that addresses this issue, where people on both sides - the administration, when they filed suit against North Carolina, were basically responding to something the governor - a suit the governor filed earlier that same day.

PETE WILLIAMS: All right.

Thank you all.

Thank you very much.

That's going to have to do it for now.

Our conversation will continue online on the Washington Week Webcast Extra.

And among the topics we'll be discussing, a setback for Obamacare and how Bernie Sanders is quietly planning to be heard at the Democratic Convention.

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

I'm Pete Williams, in for Gwen Ifill.

Good night.