MARTHA RADDATZ: Big wins for the front-runners as they eye a general election fall campaign, plus the president's make nice overseas trip, while here at home a currency makeover in the works.

I'm Martha Raddatz, in for Gwen Ifill, tonight on Washington Week.

From humble winner - DONALD TRUMP: (From video.)

This has been an amazing week.

We don't have much of a race anymore.

MARTHA RADDATZ: Donald Trump says he's ready to be more presidential, but is he?

DONALD TRUMP: (From video.)

In the case of "lyin' Ted" Cruz - "lyin' Ted" - lies.

Oh, he lies.

I love running against crooked Hillary.

I love that.

MARTHA RADDATZ: The GOP front-runner's new strategy, with an eye toward the fall.

While the Democratic front-runner is turning her focus to her potential GOP rivals.

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

Donald Trump and Ted Cruz are pushing a vision for America that's divisive and, frankly, dangerous.

MARTHA RADDATZ: Overseas, some presidential fence-mending.

PRESIDENT BARACK OBAMA: (From video.)

The alliance between the United States and the United Kingdom is one of the oldest and one of the strongest that the world's ever known.

MARTHA RADDATZ: But how are the president's comments about global free riders going over with U.S. allies?

And a new face on a familiar place.

TREASURY SECRETARY JACK LEW: (From video.)

It's been over a hundred years since we've had a woman on our currency.

And that had to change.

MARTHA RADDATZ: Who's on, who's off, and why now.

Covering the week, Dan Balz, chief correspondent for The Washington Post; Doyle McManus, columnist for The Los Angeles Times; Carol Lee, White House correspondent for The Wall Street Journal; and Eamon Javers, Washington correspondent for CNBC.

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, Martha Raddatz of ABC News.

MARTHA RADDATZ: Good evening.

New York turned out to be a special place for the two party front-runners this week.

Hillary Clinton won 58 percent of the vote and nearly that same percentage of the delegates in the state she represented in the U.S. Senate for eight years.

And after a rocky couple of weeks, New Yorker Donald Trump topped the 60 percent mark and swept almost all the delegates in his home state as he marched closer to the GOP nomination.

DONALD TRUMP: (From video.)

Senator Cruz is just about mathematically eliminated.

(Cheers, applause.)

And we've won another state.

As you know, we have won millions of more votes than Senator Cruz, millions and millions of more votes than Governor Kasich.

We've won, and now - and especially after tonight, close to 300 delegates more than Senator Cruz.

(Cheers, applause.)

We're really, really rocking.

MARTHA RADDATZ: So, Dan, is he really, really rocking?

What do you see as the state of the race right now?

DAN BALZ: Well, he really rocked in New York.

And to break that 60 percent barrier was pretty significant and I think it caught a lot of people's attention, and in an important way kind of changed the nature of how people now see the race.

There's still a question of whether he can get to the 1,237 votes he needs to win the nomination in Cleveland in July.

His campaign says they are going to get there.

They're going to get there relatively easily.

It will be clear within a matter of weeks that they're going to be able to do that.

His rivals say that's still a very heavy lift on his part.

This is going to go all the way to California.

We won't know until June 7th or June 8th, or perhaps shortly after that, whether he's going to be able to do it.

But he took a big step this week.

MARTHA RADDATZ: And how is the party establishment preparing for that?

You were just down with the RNC in Florida for meetings down there.

DAN BALZ: I was.

They met this week.

And it's curious, on the one hand they're definitely preparing for a contested convention.

They have to because, you know, as this thing is sort of touch and go.

And so everything they are putting out publicly is this is going to be fair, the rules will be enforced, everybody will have - play on a level playing field.

This is not a rigged system.

Chill out.

Behind the scenes, there is - there is what I would say the beginning of an accommodation to the idea that it's going to be Trump.

That makes a lot of people nervous.

They are trying to figure out what that really means for the party in the fall.

But you can see that after New York more and more of them think, whether they like it or not, he's going to be their nominee.

MARTHA RADDATZ: And, Doyle, are we going to see a new Trump, the more presidential Trump that Paul Manafort's saying he was just playing a part up until now?

DOYLE MCMANUS: Well, we've already seen glimpses of the new Trump, Martha.

And Donald Trump has spent weeks and weeks saying that he can be presidential and that at the right point, when he's got this thing locked up, he will pivot and be more presidential.

Now, in a sense, what he said in New York - what he said, well, Ted Cruz has how been mathematically eliminated means he's approaching the pivot point.

It depends on how you count.

Ted Cruz has nearly been eliminated but, you know, that doesn't mean that Donald Trump getting to 1,237 is a lock.

So this is - this is really quite fascinating.

He has - he has occasionally been a little more statesmanlike.

He has begun scheduling a set of speeches about important policy issues, beginning with foreign policy, to prove that he really has been thinking about becoming president of the United States.

He's actually going to read those speeches from a text with a teleprompter and everything.

So watch this space.

Now new can the new Trump be?

But here's the other problem.

You can't un-ring a bell.

And Donald Trump spent the early part of this campaign talking about Mexicans as rapists, talking all kinds of trash about the Republican Party and everybody he didn't like.

Those impressions aren't going to go away.

CAROL LEE: Now, if - he's saying that he's playing a part.

Obviously a lot of people voted for him playing that part.

Typically, that's an accusation that your opponent would make against you, that you're a flip-flopper.

Does that hurt him?

Or is this just another instance where he can get away with things that are - DOYLE MCMANUS: Yeah, that's part of the - Carol, that's part of the wonder of Donald Trump, that he can get away with things that ordinary mortals can't.

But there's also - you know, I think the serious part - your question is right.

There's a tension there.

How statesmanlike can Donald Trump be without some of his followers feeling he's abandoned them, because they liked the fact that he was going to fight for them.

And that's really the tension he's got to make his way through.

EAMON JAVERS: What about the whole Senator Cruz thing, and then switching back to "lyin' Ted"?

He tried to be respectful.

You saw that, Senator Cruz, Senator Cruz, again and again.

And then maybe he couldn't help himself?

Or what was it?

Suddenly Donald Trump is talking about "lyin' Ted" again out on the campaign trail.

DOYLE MCMANUS: Yeah, and maybe that means he's not really sure that Ted Cruz is gone, right?

DAN BALZ: I think that's probably right.

I mean, he's still prosecuting a campaign.

And everything we've seen in the course of this campaign is that when he's in a fight, he fights hard and he will throw everything he can at his opponents.

He knew on Tuesday night he had to be magnanimous, but he doesn't have 1,237 at this point, and he needs to move on.

MARTHA RADDATZ: OK, let's talk about that other side.

On the Democratic Party side, the upshot of Hillary Clinton's big win was twofold.

First, it brought her closer to the needed number of delegates to wrap up the nomination.

And it also made things much more difficult for rival Bernie Sanders to see a path for himself and his followers.

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

Next Tuesday there will be a very important primary here in Pennsylvania.

(Cheers, applause.)

If there is a large voter turnout, I believe we will win.

(Cheers.)

HILLARY CLINTON: (From video.)

The race for the Democratic nomination is in the home stretch and victory is in sight.

(Cheers.)

And to all the people who supported Senator Sanders, I believe there is much more that unites us than divides us.

(Cheers, applause.)

MARTHA RADDATZ: And so, Doyle, it sounds like he's still fighting, and she's inviting.

DOYLE MCMANUS: Absolutely.

Two completely different songs.

Hillary Clinton would like this race to be over.

She would like to stop having to spend money on this race.

She would like to stop having to worry about Bernie Sanders.

She would like to start - she is already inviting his followers to come back into the Democratic fold, which she desperately needs for that general election campaign, which is the campaign she wants to talk about.

Bernie Sanders knows that he's got an incredibly tough path.

He has to win about 59 percent of the remaining delegates, and those are just the pledged delegates.

That's not the superdelegates.

That's an almost impossible task.

That's why we have all started saying, well, she's pretty close to getting it locked up.

Lighting would have to strike, and it would pretty much have to strike Hillary Clinton right on the head, for it not to work for her.

MARTHA RADDATZ: And, Dan, you asked this week in one of your stories: What does Sanders want now?

DAN BALZ: I think it is the big question.

I think everybody knows that this race is going to go through all of the primaries.

Senator Sanders has earned that right, as Secretary Clinton earned that right in 2008.

But at a point in the race in 2008 when it was clear that she could not win, which was in early May of 2008, she told her campaign team: We're going to fight to the end, but I'm not going to do anything that would make it more difficult for president - for then-Senator Obama to win the general election.

And I think one of the questions now is, how will Senator Sanders conduct himself for the rest of the campaign?

Will he continue to prosecute the case in the way he did over the last few weeks, which made a lot of Democrats nervous that those attacks went from policy to, in a sense, touching on character.

And there are people not just in the Clinton organization, but within the party, who are worried about that.

But Sanders also has done something remarkable in this campaign.

I mean, the success he has had has made him a very important figure.

And he's got a lot of assets that he's got think about how he wants to use them in the future.

EAMON JAVERS: If the lights are going out slowly on the Sanders campaign, as you guys are suggesting, what does it mean in Pennsylvania?

Carol and I are both from Pennsylvania originally, so we have a vested interest in finding out how significant the state is.

But what would it mean if Bernie Sanders were to come up with a win in Pennsylvania?

I mean, that may be a long shot, but can he turn the tide in any way at this point?

DAN BALZ: I think it - it would be a surprise if he wins.

I think she's set up to have a pretty good day next Tuesday in Pennsylvania and the other states that vote.

But if he were to do that, it would be one more question mark about her, and it would reinvigorate him to continue the kind of campaign he's been running.

So I think - I mean, for Clinton, it would be a terrible moment.

She would still be the odds-on favorite to be the nominee, but it would mean more trouble - EAMON JAVERS: So Pennsylvania matters, is what - DAN BALZ: Pennsylvania matters.

DOYLE MCMANUS: Sure.

And just to play with the hypothetical, you know, the national polls have been narrowing.

And some late-deciding Democrats have been moving in Bernie Sanders' direction.

California is the last contest here.

And Californians take a long time to notice that an election campaign is going on.

(Laughter.)

California - if Pennsylvania is an upset, if other states next week are an upset, California could be real race and, who knows?

CAROL LEE: So how long can this go on before it becomes really damaging in November for the Democrats?

DAN BALZ: That's a great question.

And I don't think anybody knows the answer to that.

Again, it party depends on what the tone and tenor of the race is.

If it is an extension of the debate that took place in Brooklyn before the New York primary, then the Democrats have a big problem coming together.

But a lot of this will have to do with how close Sanders is able to get, what the talk is between the Sanders campaign and the Clinton campaign, and the degree to which both of them are prepared to make accommodations to one another.

DOYLE MCMANUS: Part of the problem here is that Bernie Sanders' campaign always had two different goals.

One was to see if he could get the nomination, but the other was to build a movement on the progressive, leftist side of the Democratic Party.

And to build that movement, he has to keep talking about a corrupt campaign finance system.

And that makes it harder to get everybody back together.

MARTHA RADDATZ: I think you'll probably hear more on that over the coming months.

(Laughter.)

Meanwhile, President Obama is in the midst of a multi-capital, Middle East and European trip, designed to calm some of the ruffled feathers with a number of allies.

In London today, he stood side-by-side with British Prime Minister David Cameron to affirm the alliance between the two countries, but to also weigh in on the controversial topic of whether Great Britain should remain a member of the European Union.

That referendum will be before voters in the U.K. in June.

PRESIDENT OBAMA: (From video.)

The United States wants a strong United Kingdom as a partner.

And the United Kingdom is at its best when it's helping to lead a strong Europe.

It leverages U.K. power to be part of the European Union.

As I wrote in the op-ed here today, I don't believe the EU moderates British influence in the world, it magnifies it.

MARTHA RADDATZ: The trip comes on the heels of an interview with Mr. Obama in The Atlantic, where he referred to "free riders" across the globe who are not necessarily pulling their weight.

So, Carol, fence mending, damage control.

There's clearly a two-pronged approach to this trip.

How'd he do?

CAROL LEE: That's right.

Well, he had a warm reception in London.

And you know, it remains to be seen how he did in terms of convincing British people to go his - vote his - the way he wants them to vote on whether or not they should stay in the EU.

This is something that the White House is very concerned about, and frankly it's the main driver of the reason why he went there.

MARTHA RADDATZ: He's been so public.

And he's got this op-ed.

That's so unusual.

CAROL LEE: It's really remarkable.

It's a remarkable thing to watch a president of the United States go to another country, stand there, and tell them essentially how to vote.

And you know, it could have some backlash.

There are people there who really didn't like that.

So it's not clear exactly, you know, how - what and how much influence that's going to have.

But the White House is very concerned about if the - if this vote were to go in the direction where the U.K. goes out of the EU, you know, it could bring economic headwinds to the U.S.

It's coming at a time when Europe is having a number of different crises, you know, with terrorism, with the refugee crisis.

Their economy is still not functioning as well as the U.S. economy.

And so he felt really strongly that he needed to go there and basically tell them to not do this.

EAMON JAVERS: One of the things the president said today when he was over there, which I think will get a lot of attention, is that if the U.K. is on its own, independent, negotiating trade deals with the United States, and the EU is negotiating those trade deals at the same time, the U.K. goes to the back of the queue, he said, using the British phrase for a line.

CAROL LEE: Yeah, it was very interesting.

EAMON JAVERS: I thought that was a fascinating moment.

Was that a veiled threat to the British?

CAROL LEE: It was - I mean, it was - yes, right?

EAMON JAVERS: Right?

CAROL LEE: And it was also putting it in perspective.

You know, you guys think this thing is going to be so great if you get this independence, and that you're going to come over and negotiate your own deals with this.

Well, we're negotiating - I mean, it's a massive trade deal that they're negotiating with the EU.

And you know, that's going to take time.

We've seen how long trade deals take.

So if you think we're going to start on something new right away, it's just not going to happen.

DAN BALZ: Carol, was this a close call within the White House about deciding to get into the middle of a very controversial debate in Great Britain right now?

CAROL LEE: No, and only in the sense that I think you've seen this president be less and less cautious as things move.

And when he feels very strongly about something, and that he can be influential, whereas maybe in the first term or early in his second term he might not weigh in, he's increasingly willing to do that.

DOYLE MCMANUS: Carol, the - MARTHA RADDATZ: And of course, he also went to Saudi.

That's pretty controversial too.

DOYLE MCMANUS: And I want to ask about that, Carol, because that Saudi-American alliance is probably the scratchiest alliance in the whole world.

The Saudis have been furious at Obama for making the nuclear deal with Iran.

President Obama has been pretty open about, you know, wondering why do I have to put up with these characters since we don't even need their oil anymore?

Did the relationship get any less scratchy because of this visit?

CAROL LEE: I don't think it gets less scratchy because of one visit.

You know, they did smile in front of the cameras and give statements and, you know, the White House felt that they had at least mended some of the fences.

But you know, he - the president - the way he has talked about Iran, in particular - for the Saudis, it's all Iran.

The engaging Iran, different things that he said in The Atlantic interview.

You know, he said that they should share the neighborhood, that they should have a cold peace.

And that just - that, to the Saudis, is unthinkable.

And in that - and all of that comes on the heels of them just not feeling like the president respects the status quo American alliances in the Middle East.

MARTHA RADDATZ: And the proposed legislation on the Hill - CAROL LEE: Yeah, and then - MARTHA RADDATZ: - whether or not Saudis could be prosecuted for any involvement in 9/11.

CAROL LEE: Right.

And the White House opposes that, because their argument is that it would put U.S. officials and diplomats overseas at risk.

But that was coming.

The declassification of some of the congressional - the congressional report on the Saudis, and all of that.

And then you had the White House having to answer these questions.

And some of the president's - ahead of this visit - and some of the president's senior advisers, you know, having to say that there were connections.

You know, all of that stuff from post-9/11 was kind of dredged back up at this very moment when the relationship is really strained.

MARTHA RADDATZ: OK, and we've got to show you this adorable picture.

(Laughter.)

The cutest picture of the trip, OK?

Little Prince George there.

It looks to me like he's in his bathrobe, his dad there.

Can't see his mom, which I'm sure disappoints.

That's pretty sweet.

CAROL LEE: He stole the show.

And he had this - MARTHA RADDATZ: Totally stole the show.

I know, I saw that today.

It was my favorite - EAMON JAVERS: What a cutie.

MARTHA RADDATZ: - favorite part of the trip.

All the rest was pretty fascinating, too.

Thanks so much Carol.

And finally tonight, the currency debate.

If you watched the Webcast Extra last week, you knew that the Treasury Department was close to a decision on some changes.

Secretary Jack Lew made it official this week, announcing that the $20 bill would be getting a major makeover, adding civil rights leader Harriet Tubman to the front of the bill.

SECRETARY JACK LEW: (From video.)

Here a woman born a slave, illiterate her whole life, can, after spending countless trips going back and forth freeing people on an individual basis, work for the Army to help - you know, as a spy, you know, help them find their way into battle in the Civil War, and then be a founder of the women's suffrage movement, how that can change our country.

And I think that's a - that's a tremendous American story.

MARTHA RADDATZ: So Andrew Jackson gets the boot, and all this time we thought Alexander Hamilton was going to be displaced from the $10 bill.

Eamon, how did this happen?

EAMON JAVERS: You know, Jack Lew bit off more than he could chew here.

He announced that he was going to take an inventory of what people thought and put a woman on the front of the $10 bill.

There was this hue and cry from all these Hamilton supporters who said, how can you possibly do this?

We love Hamilton.

What are you doing?

It - MARTHA RADDATZ: Who'd all seen the musical, yeah.

(Laughs.)

EAMON JAVERS: It's the musical on Broadway.

It's a runaway smash hit, and now it's affecting our actual currency.

So Jack Lew said he had an "a-ha" moment.

He sat back and said, maybe this isn't just about one bill; maybe we can redesign a bunch of bills and solve all of these problems.

So the end result is we're going to get a new-looking $5 bill, we're going to get a new-looking $10 bill, and we're going to get a new-looking $20 bill.

So Harriet Tubman goes on the face of the $20 bill.

That's going to be the first African-American ever on the face of U.S. currency.

DOYLE MCMANUS: Was it - was it really the musical - (laughs) - that changed this?

EAMON JAVERS: I think it was.

It was.

I mean, there are not a lot of Hamilton fans out there in normal daily American life - (laughter) - but suddenly this musical got a lot of attention, and people were mobilized to defend Alexander Hamilton.

There was also a movement to put a woman on the face of a bill, and Jack Lew had to wrestle with all that.

And this is sort of the compromise that he came down with, is you put new backs on some of the bills, new fronts on the 20, and now we're going to have an entirely new look for our currency.

DOYLE MCMANUS: And so why did Andrew Jackson turn out to be the loser?

You know, anytime you make a bunch of changes, somebody's going to be unhappy.

So who got left out here?

EAMON JAVERS: Well, some Tennessee politicians don't like this decision to move Jackson off.

This guy is the big loser here, on the face of the 20.

The 20's going to look a lot different.

But ultimately, it's a popularity contest, right?

I mean, this is about a nation sending its image into the world of what it wants to be - not only how it wants to view its past, but how it wants to view its future.

And that's what this decision is about.

MARTHA RADDATZ: OK, this would take a very long time for this to happen.

EAMON JAVERS: Yeah.

MARTHA RADDATZ: In the meantime, you're going to have a new president.

EAMON JAVERS: Yeah.

MARTHA RADDATZ: Let's listen - not saying he's going to be the new president, but he has a shot.

Let's listen to what Donald Trump had to say about this.

DONALD TRUMP: (From video.)

I would love to leave Andrew Jackson and see if we can maybe come up with another denomination.

Maybe we do the $2 bill or we do another bill.

I don't like seeing it.

Yes, I think it's pure political correctness.

MARTHA RADDATZ: And?

EAMON JAVERS: Well, Jack Lew says he doesn't think the next administration, no matter who it is, is going to reverse this decision.

They admit that they only have a few months left in the Obama administration.

The calendar is a fact.

But they think the politics of this are such that no administration, whether it's Trump or anybody else, is going to want to be the administration that pulled Harriet Tubman off of U.S. currency.

CAROL LEE: Do you know - when is the last time that this - faces on a currency were changed?

And was there this let's all share the currency kind of debate?

Or is that just a new cultural - EAMON JAVERS: That's a really good question.

I don't know the answer to that.

I know that there was a woman on U.S. currency before.

It was Martha Washington.

But it hasn't been for a hundred years that we've had a woman on the face.

MARTHA RADDATZ: They didn't have a musical back then, so.

EAMON JAVERS: And they didn't have a musical, right, so.

But, look, it matters, ultimately.

Your currency is sort of how you're seen in the world.

And if you look at the British pound, they have pictures of the queen on there because that's a country that wants to be seen as a country that has a queen and they think that's important.

You look at the euro, and the euro has just anonymous buildings and bridges and things on it - you can't even tell what country they're from - because that's an entity that can't decide what it wants to be and can't agree on its collective history.

So who you put on your currency says a lot about who you are as a society, and we're now saying that we're a society that includes Harriet Tubman.

DAN BALZ: Assuming no changes, when will we see Harriet Tubman on the bill?

EAMON JAVERS: It won't be until about 2020, so we're looking at a long - MARTHA RADDATZ: Or maybe even 2030.

EAMON JAVERS: We're looking at a long rollout here.

And the $10 bill's going to actually be the first one to be changed because they have to change all the security features because there's so much counterfeiting that's going on right now.

It's rampant.

MARTHA RADDATZ: OK. And thanks to all of you.

That will have to wrap it up for tonight, but we have more on the Washington Week Webcast Extra, where among other things we'll talk about Prince.

That's later tonight and all weekend long at PBS.org/WashingtonWeek.

Keep up with news developments each night with the PBS NewsHour, and we'll see you around the table again next week on Washington Week.

I'm Martha Raddatz.

And to those celebrating, here's wishing you a Happy Passover.

Good night.