JUDY WOODRUFF: As we heard earlier, President Obama, during a trip to the United Kingdom in April, said that it should stay in the European Union.

Today, from Stanford University in California, the president gave his appraisal of yesterday's outcome.

PRESIDENT BARACK OBAMA: While the UK's relationship with EU will change, one thing that will not change is the special relationship that exists between our two nations. That will endure.

The EU will remain one of our indispensable partners. Our NATO alliance will remain a cornerstone of global security, and in a few weeks, we will be meeting in Warsaw for the NATO summit. And our shared values, including our commitment to democracy and pluralism and opportunity for all people in a globalized world, that will continue to unite all of us.

JUDY WOODRUFF: The president spoke with David Cameron by phone today, and, according to the White House, expressed regret that his — quote — "trusted partner and friend" decided to step aside as prime minister.

Mr. Obama also spoke with German Chancellor Angela Merkel. The two leaders said they regretted the UK's decision to leave the EU, but that they respected the will of the British people.

Now there are serious questions about how this break may change the current of global politics.

We explore what may lie ahead with Ivo Daalder. He's a former U.S. ambassador to NATO. He's now at the Chicago Council on Global Affairs. Richard Haass is a former State Department and top National Security Council official. He now runs the Council on Foreign Relations. And Margaret Warner, the "NewsHour"‘s chief foreign affairs correspondent.

And welcome to all three of you.

Richard Haass, I'm going to start with you.

We just heard two guests say that this could be the end of an era in terms of global economics. What about in terms of the politics of this globe?

RICHARD HAASS, President, Council on Foreign Relations: Well, I think historians will look back on this, and this will be something of a defining or dividing line in terms of the U.S.-UK relationship.

The president can use the rhetoric about it being special, but the fact is, it isn't very special anymore, and Britain won't have the capacity to be a real partner, particularly, as I think is likely, Scotland ultimately leaves and potentially even Northern Ireland leaves, so the United Kingdom becomes the disunited Kingdom.

It's also very bad for what's going on in Europe. It's not just economic integration, but it's the entire European project, and now lots of other countries may decide to find their own path to distance themselves from Europe.

And that's a big part of the post-World War II architecture. It's one of the great accomplishments of modern diplomacy, to make Europe stable and prosperous. So, I actually think the last 24 hours, whatever the voters had in mind, wanted message they wanted to send to elites and establishment, they set in motion a dynamic that will really detract from prosperity and stability, I think, in Europe and conceivably beyond.

JUDY WOODRUFF: Ivo Daalder, how do you see the political~ fallout?

IVO DAALDER, Former U.S. Ambassador to NATO: Well, I think it is potentially grave as Richard is implying.

I think what we're seeing is not only the return of nationalism in the United Kingdom, and particularly in England, but that nationalism can spread throughout the continent. And you have already seen calls in the Netherlands for a referendum there, for a Nexit. You have seen the same in France for a possible referendum for France to leave the Union.

And what you see is nations turning inward, becoming more nationalistic, wanting to be self-reliant, breaking away from the European Union. And, as a result, you get the kind of re-nationalization of European politics that we saw in the '20s and the '30s. And we know what the consequences of that was.

So there is the very real possibility of this spreading to the continent with more and more countries trying to leave the union, trying to turn inward, finding it difficult to achieve what they want to achieve, and therefore turning against each other.

JUDY WOODRUFF: Well, some of this sounds fairly dire.

Margaret, I know you have been talking to a number of U.S. officials today. How do they see the effect of all this politically?

MARGARET WARNER: Very much the way Richard Haass and Ivo Daalder do.

Today, when he we heard what the president had to say, one official said to me, well, that was no drama Obama. But in the weeks leading up to this, as it got close, intelligence, diplomatic and defense officials all were very — were filled with dread really about the consequences of this.

I mean, nothing will change in terms of the UK being a major partner. I mean, this is a country that we share language and culture and world view. But, as Richard said, the concern is that it will be a less effective partner, that is, that Prime Minister Cameron and whoever succeeds him will be a distracted partner, that they will be potentially weaker because there will be — if there's a breakup in the British Isles, and also a poorer partner, as one official said to me, who may not even be able to make the 2 percent threshold in NATO.

So — and, finally, of course, there's the whole question about whether it weakens U.S. diplomatic leverage in Europe. Now, some people feel that's been overstated. It wasn't terribly effective to work through Britain, say, to get Germany last year to soften the terms for Greece.

But, still, with Europe — with the UK having a seat at the table, the U.S. had at least eyes on the table, and that won't be true anymore.

JUDY WOODRUFF: Richard Haass, how much at this point depends on how this is handled by world leaders, whether it is by the British leadership, by people like Chancellor Merkel, President Obama? How much could that affect what happens?

RICHARD HAASS: Not all that much, I'm afraid, Judy.

In terms of the British, they have got really limited discretion. It's very hard for a prime minister, for Mr. Cameron's successor, for the Parliament to somehow ignore the — quote, unquote — "will or voice" of the British people.

And then, looking at it from the other side, I don't think Brussels is going to necessarily tell the British, well, never mind, or somehow set a precedent that then 27 other countries might say, OK, we can then define our own relationship. Let's have an a la carte relationship that lets us choose A, B, C, but we will ignore D and F.

So I actually think, on both sides, the hands are relatively tied. And I know this sounds pessimistic. And there are people who are saying just maybe we can work through this and it wasn't that definitive, but I actually don't think so.

And even if there is considerable voters' remorse — and I expect there will be something of a collective hangover once the reality sinks in of the repercussions — I still don't think even the British side or the European side are going to have that much discretion.

JUDY WOODRUFF: Ivo Daalder, pick up on that. What do you see could determine whether this goes in an even darker, or more disturbing direction? What could keep things on track? I mean, who has the ability to determine which direction it goes?

IVO DAALDER: So, I agree that there is not much leverage or capacity in Britain, certainly with a lame-duck and now defeated prime minister still on the helm, and then a victor coming in who really doesn't know what needs to be done.

But I don't necessarily agree that there isn't any leverage or room for maneuver, particularly with Chancellor Merkel and with the United States.

Stepping back, we have been at this 70 years. This is not just a European project. It's very much an American project, and we have been central for those 70 years to cajole the Europeans at particular times, when things were going the wrong way, to do the right thing and work together.

Our leverage isn't the same as it was in the '40s, and the '50s and the '60s, but it's still there. We're still a very critical partner. And I do believe that, if the United States, particularly working together with Chancellor Merkel, were to make it very clear that, yes, we accept the results of the voters, and, yes, there will be a different relationship between the United Kingdom and the European Union, but we still want the United Kingdom to be a fundamental, strong European power, and we want the Europeans and the United Kingdom and the United States to work closely together — we will do it in NATO.

We will do it on an ad hoc basis outside of it, but we need to work this out together in order to maintain this — the essential European project that was started 70 years ago. It's a defining moment for American diplomacy.

JUDY WOODRUFF: And, Margaret, in talking to U.S. officials, do they recognize that? Are they prepared to move in that direction?

MARGARET WARNER: Very much so, Judy.

As Ivo Daalder just said, the American security for 70 or 80 years has relied on a strong, prosperous, united Europe that we spent billions, trillions, I guess, through the Marshall Plan on forward, and diplomatic years and decades to help establish.

And then you recall, after the Soviet Union collapsed, the way to get the Central and East European countries as part of this, with all their ethnic conflicts and everything, was the carrot of EU membership. That was the incentive.

So it's been very, very important. What U.S. officials are hoping, going back to Richard Haass' point, about buyer's remorse, is that, if the train can be slowed down of a lot of other countries clamoring to do this, that other Europeans will witness what happens to Britain now, and it probably won't be a pretty sight in the medium term.

JUDY WOODRUFF: Well, there is much more to unfold.

And we want to thank all three of you for taking a look with us tonight.

Margaret, Margaret Warner here, Richard Haass, Ivo Daalder, we thank you.

RICHARD HAASS: Thank you.