ANNOUNCER: This is the Washington Week Webcast Extra.

GWEN IFILL: Hello, I'm Gwen Ifill.

Welcome to the Washington Week Webcast Extra.

I'm joined around the table by Pete Williams of NBC News, Karen Tumulty of The Washington Post, and Peter Baker of The New York Times.

After months of relaxed access to Cuba, the president heads there next week to make policy and to make a point.

What does this move toward normalization, even while the Castro brothers are still alive, mean, Pete-r?

PETER BAKER: Yeah.

(Laughs.)

GWEN IFILL: There are too many Petes at this table.

(Laughter.)

PETER BAKER: I'm good with Pete.

Pete's OK with me.

President Obama really wanted to go to Cuba.

This is one of the things he's wanted to do since he's been in office, and it's a historic moment.

There are very few places left that a president gets to go to that seem big, like Nixon going to China, and Cuba is one of them.

Now, the criticism is, of course, that he's going there without having gotten anything for it - that, in the year and so many months that he has opened diplomatic relations, that the Cubans haven't relaxed any of the oppressive rules on their own people, that they haven't actually made things better in terms of human rights, and that the president's kind of, you know, being played here.

The argument the president makes is it's a long process.

And, yes, we haven't seen as much progress as we would like, but the very sign - very sight of an American president coming to Cuba will say this is a different era, we're changing things, and ultimately over the long term will make a difference.

GWEN IFILL: I remember at Nelson Mandela's funeral when everybody was upset about the sign language interpreter who wasn't actually sign language interpreting.

The president shook Raul Castro's hand.

And I remember thinking, wow, no one noticed that that just happened?

And that was kind of the first - the first of this, as far as we know, opening.

PETER BAKER: Yeah, it was.

And he'll see Raul Castro while he's there in Havana.

He will not see Fidel Castro.

That's been on the no-go list in terms of the negotiations about what this trip will be about.

That's a step too far, still, in American politics.

But, you know, he's met with Raul a couple times.

He met with him now last year at the Summit of the Americas.

And they have - you know, I wouldn't say they've got a close friendship or relationship, but he's trying to create the idea that we should have a working relationship.

GWEN IFILL: Was this on the Obama administration's bucket list?

PETER BAKER: It definitely was, yes.

And there are not a lot left for him in the next 10 months in terms of foreign policy.

He's not likely to go to Tehran.

We're not likely to ever get close enough.

GWEN IFILL: Guantanamo's not likely to close.

PETER BAKER: We're not likely to close Guantanamo.

And so this is sort of like the biggest sort of spectacle kind of moment left he's got.

GWEN IFILL: Karen, I want to go back to politics with you for a moment, because inherent in this stop Trump idea is that somebody else can step in.

Assuming that it's not someone currently running, it was John Boehner's bright idea this week - as has been others in the past - that it should be Paul Ryan, the speaker of the House.

Let's listen to what he said about that.

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

I saw Boehner last night and I told him to knock it off, you know?

(Laughter.)

I used slightly different words.

I used his own words that he used to use against us when he told us to knock things off.

It's not going to be me.

It should be somebody running for president.

Look, I made a decision over a year ago not to run for president.

I really believe, if you want to be president, you should run for president.

GWEN IFILL: He also made the decision six months ago not to be speaker of the House.

(Laughter.)

KAREN TUMULTY: Exactly.

You could have - GWEN IFILL: So what are we to think?

KAREN TUMULTY: Well, I do think that it would be difficult for somebody who hasn't even been in, you know, as it were, in the arena to step in.

But certainly, you know, Paul Ryan has become the face of Republican governance.

I mean, he's become - to the degree that the Republican Party - GWEN IFILL: Which is the problem, isn't it?

KAREN TUMULTY: True, but to the degree that the Republican Party at this moment stands for any actual ideas and any actual policies, those are Paul Ryan's ideas and policies.

So you can certainly see why the idea would have some appeal.

And then there are all kind of convention rules about, you know, whose names can actually be put into nomination.

They've got to - GWEN IFILL: They've got to have won eight states, right?

KAREN TUMULTY: You have to have won a majority of delegates in eight states.

That rule is almost certain - it will be rewritten for this convention.

And that, of course, is the other thing.

I mean, these conventions, they can just blow up all their rules and start from scratch.

So theoretically, it's possible.

GWEN IFILL: I don't want to spoil it for you if you haven't watched House of Cards, but according to the fictional part, this could happen.

(Laughter.)

OK.

(Laughs.)

I wanted to turn to you, Pete.

Give us a preview of next week.

We have a couple of big cases coming up at the Court.

PETE WILLIAMS: Right.

Well, the biggest one is another challenge to Obamacare.

You may remember that when it was started, part of it was that the health insurance would have to cover contraceptive care for women.

Now, the administration first said, well, OK, after there was some blowback, they said, all right, we'll carve churches out of that.

Churches don't have to provide that coverage; they're exempt.

But then a lot of other organizations said, well, you know, religious colleges - Notre Dame, Georgetown - the Little Sisters of the Poor, what about us?

So the administration said, OK, here's all you have to do.

You fill out a certain form saying that you find this a religious burden, this would violate your religious principles, and then you don't have to do this.

Little Sisters of the Poor said that's still not good enough because that still makes us complicit.

So the Supreme Court said - OK, Little Sisters, all you have to do - you don't have to sign the forms, just give us a note and tell us the name of your insurance company, the government says.

So here's the question: Does doing that, is that still enough to violate their religious principles?

And the government says no.

You're opting out.

You don't pay for the coverage anymore.

You have nothing to do with deciding who gets it.

The Little Sisters and the other organizations - there are dozens of religiously affiliated organizations, colleges, universities, charities - they say it's still our health plan that's being used to provide this coverage, we're not out of it.

We're, in essence, opting in, and that violates our religious principles.

So the Supreme Court's going to have to decide who's right there.

GWEN IFILL: Four to four.

PETE WILLIAMS: Well, it could be 4-4, although I will tell you that the lawyers on both sides doubt that it will be.

Even though it was 5-4 when this question was asked about - GWEN IFILL: Hobby Lobby.

PETE WILLIAMS: - you know, for-profit companies that are closely held and strongly religious views of the family that owns them.

It was 5-4, you take away Antonin Scalia, you'd think it's 4-4.

But there are a lot of different equities here.

And, you know, Sonia Sotomayor showed some inclination to be sympathetic, so we'll see how it goes.

GWEN IFILL: OK. Well, thank you all again.

And thank you all for watching as well.

While you're online, check out everything else our panelists are covering in News You Need To Know.

That's every day at PBS.org/WashingtonWeek.

And we'll see you next time on the Washington Week Webcast Extra.