NICK SCHIFRIN: The war in Iran has opened new cracks in President Trump's relationship with GOP leaders on Capitol Hill, and Democrats face their own family feud this week as New York's primaries pit progressives against moderates.

Here to reflect on that and the Reflecting Pool is our Politics Monday duo, Amy Walter of The Cook Political Report With Amy Walter and Tamara Keith of NPR.

Thanks, guys.

Welcome back.

AMY WALTER, The Cook Political Report: Hello.

NICK SCHIFRIN: Tam, let me start with you.

You have got high-profile Republican allies questioning the Iran memo of understanding, say it's weak.

And there's also spy power negotiations at a standstill.

Is this a GOP Conference now pushing back or not?

TAMARA KEITH, National Public Radio: I think that we need to wait a little while to see whether they are rhetorically pushing back or whether they're actually going to take votes or do more substantive things to push back on the president.

They certainly have -- some of them have certainly expressed displeasure with the Iran deal, with President Trump, like, temporarily pulling his nomination for the director of national intelligence or telling him not to show up for his confirmation hearing.

There is a big well of frustration with Republicans towards the president.

There's a big well of frustration from the president towards Republicans, insisting that they do all kinds of things to pass the SAVE America Act... TAMARA KEITH: ... which is a measure that would require voter I.D., proof of citizenship, and also would really limit mail ballot, mail voting, which a lot of Republicans actually like.

He's putting a lot of pressure on Senate Republicans.

He's actually headed up to the Hill this week to meet with some of these Senate Republicans.

It's just not clear that they can give him what he wants, but it's also not clear how hard they're ultimately going to push back against him.

NICK SCHIFRIN: Amy, I wonder how much political pressure there is from people, so to speak.

Let's look at the polls.

AMY WALTER: The people.

NICK SCHIFRIN: The people.

"PBS News Hour"/NPR/Marist poll released last week found the president with the lowest approval rating of his second term, 36 percent, only 33 percent approving of his handling of the economy, a new low for him as president.

And 78 percent of Americans say gas prices are straining their household budget.

How much of this is actual pressure?

AMY WALTER: So, here's where this Republican rift is really interesting.

As we have been discussing and you know very well, there's definitely a rift ideologically on Capitol Hill between those maybe who are more hawkish, who would like to see the United States continue down the path they were going on militarily and others who did not want to see that.

But, fundamentally, politically, if you're a Republican up for reelection in a tough district, here's a number you have been seeing since the war started.

The president's handling of the economy, the net unfavorable has gone up by about 10 points.

His net unfavorable on inflation has gone up close to 20 points.

That is a problem for you as a Republican running for reelection.

So this war ending, theoretically, is going to help bring those numbers back to hopefully a reasonable place if you're a Republican running for reelection.

But the challenge right now for Republicans in the sort of intraparty challenge, beyond this question of how hard do they push back Donald Trump, who still remains the kingmaker in the party, but is the lack of enthusiasm among the base.

And the one thing in that Marist poll that I looked at is people who identify as Republican, how strongly do they approve of Trump versus how many are just like, yes, he's OK, he's fine, I approve.

The strongly approved number since a year ago at this time among Republicans has dropped like close to 12 points on net.

And so what you're seeing, is Republicans aren't abandoning Donald Trump, but they're just not as enthusiastic about him, which means they may not be as enthusiastic to show up to vote.

NICK SCHIFRIN: Let's talk about Democratic primaries tomorrow.

Maryland, Utah hold primaries tomorrow.

South Carolina hold its primary run-off.

But most election watchers will be focused on New York, where New York City Mayor Zohran Mamdani is backing challengers against incumbent Democrats he sees as too moderate.

Amy, which races are you watching most closely?

AMY WALTER: Well, let's start with this.

Yes, it's New York.

I love the people of New York, but it is a very small segment of the electorate.

Now, no doubt, I think the national attention is going to be on Mamdani and whether he can use what he has right now, which is considerable political clout within the -- New York City's progressive movement, to get his preferred candidates over the line.

I'm intrigued by a couple of things.

The first is there's basically an A.I.

versus A.I.

battle taking place in one of the districts in Manhattan, Upper West, Upper East Side, where the folks from Anthropic who would like to see maybe more regulation are supporting a candidate who while in the state legislature actually passed some A.I.

regulation.

The folks at OpenAI don't really like the legislation that he passed and so they're spending against him, millions and millions of dollars for one seat in Congress.

The second thing I would say, there's a lot of talk about whether Mamdani succeeds.

What does this mean for the Democratic socialist movement?

Does this mean the party now, the Democratic Party, has moved so far left?

The race I think that's going to tell us much more about that is not happening until August.

And that's in Michigan, where a much more progressive candidate, sort of in the mold of some of these candidates that Mamdani is supporting, is facing off against two more sort of establishment type of Democrats in a swing state, in a state that's going to matter in the next upcoming presidential election as well.

So whether that candidate can win a primary and whether that candidate can win a general election will tell us a lot more about the strength of that wing of the party, the Mamdani wing or the Bernie wing than what's happening in New York.

NICK SCHIFRIN: In New York.

NICK SCHIFRIN: And, Tam, let me finally get you on the pool.

So the president seems... TAMARA KEITH: Why, thank you.

(LAUGHTER) NICK SCHIFRIN: Yes.

The president seems increasingly frustrated, shall we say, by his struggle to clean the pool, to convince the public that it was in fact saboteurs who created all that algae and all of the paint crusting.

Do these claims, do these arguments still land with the supporters?

TAMARA KEITH: Yes, and I will not be here to truth on or fact-check on epoxy and how it works, because that is not my expertise.

What I will say is that this Reflecting Pool has turned into yet another fight over Donald Trump.

And he made the pool about himself.

It is one of many projects that he has pushed through ahead of America 250.

He has put so much focus on it, so much, calling people into the Oval Office to show charts of the pool next to giant skyscrapers to say how big it is and on and on and on and all of these TRUTH Social posts and all of this.

That he's drawing so much attention to it, and it does raise the question, like, what about those kitchen table issues that Senate Republicans want to talk about, and this housing bill that has bipartisan support and just passed the Senate that could be something that they could run on?

AMY WALTER: Or talk about, which he has not talked about at all, right?

Yes.

TAMARA KEITH: Right, other than the pool.

AMY WALTER: Yes.

TAMARA KEITH: Anything but the pool.

NICK SCHIFRIN: I have a feeling the pool debate will continue.

(LAUGHTER) TAMARA KEITH: Yes.

NICK SCHIFRIN: Tamara Keith, Amy Walter, thanks, as always.

Appreciate it.

TAMARA KEITH: You're welcome.

AMY WALTER: You're welcome, Nick.