GEOFF BENNETT: Welcome to the "News Hour."

President Biden is facing growing calls from a handful of House Democrats to step aside as the party's presidential nominee.

Earlier today, in a rare cable news program call-in, the president addressed his critics and maintained that he was still the best person for the job.

JOE BIDEN, President of the United States: I am getting so frustrated by the elites.

Now, I'm not talking about you guys, but about the elites in the party, who -- they know so much more.

But if any of these guys don't think I should run, run against me.

Go ahead.

Announce for president.

Challenge me at the convention.

GEOFF BENNETT: Our congressional correspondent, Lisa Desjardins, and our White House correspondent, Laura Barron-Lopez, join us now.

So, Laura, President Biden is unwavering.

He says he's not exiting this race.

Give us a sense of what more he's saying and the White House strategy here to calm nervous Democrats.

LAURA BARRON-LOPEZ: President Biden's message right now, Geoff, is that he's not going anywhere.

And he sent a letter to congressional Democrats today in which he said -- quote -- "The question of how to move forward has been well-aired for over a week now.

It's time for it to end.

Any weakening of resolve or lack of clarity about the task ahead only helps Donald Trump and hurts us."

And what President Biden is saying publicly is also what campaign aides are saying privately to donors, to Democratic lawmakers, to Democratic Party officials across the board.

And that's essentially that he was the only one that has shown that he has beaten Donald Trump in the past, that the debate was one bad night, that that isn't the way he is across the board, and that he is strong enough to run this campaign.

Campaign officials have been making calls to individual donors, to lawmakers.

President Biden himself was on a call today with donors in which he also said that they can't waste any more time being distracted, that this needs to end.

He's going to speak tonight virtually with Congressional Black Caucus lawmakers.

And the campaign is pointing to a recent Bloomberg poll essentially saying that, look, that poll shows that President Biden is up in states like Wisconsin and Michigan and that their internal polling shows similar, and that, ultimately, they say the debate hasn't had an impact on where the state of the race is.

Now, White House Press Secretary Karine Jean-Pierre faced a number of tough questions today in the press briefing.

She was asked about the president's mental and physical fitness to do the job, to carry out the job.

And she said that he has been seen three times over the course of his presidency by a neurologist.

She was asked about visits over the course of eight months in the last year by a Parkinson's specialist.

And she essentially said that the president is -- has never been treated for Parkinson's, is not currently being treated for Parkinson's, and that he's not taking any Parkinson's medication.

So that is their full-court press against the backlash to the debate right now.

GEOFF BENNETT: And, Lisa, are the efforts that Laura outlined, the Friday ABC interview, the president's barnstorming yesterday in Pennsylvania, his call into "Morning Joe" today, is any of this changing the minds of those House Democrats?

LISA DESJARDINS: No, it is not.

They see these events as on friendly terms and not really as challenging as the debate.

They want to see him kind of extend himself more.

They want to be able to get a better picture of exactly how he operates in challenging situations.

Let me go over where things stand here.

Now, we know of nine House members who have called either publicly or among leadership for President Biden to step aside.

And among those in that top row are four ranking members of committees, including Adam Smith of the House Armed Services Committee.

But there was more news today from the Senate.

Speaking to senators themselves and to senior staff, chiefs of staff over there, I can say that there are right now very few Democratic senators who believe Biden should stay in as nominee.

However, there is a lot of conversation and debate in a senatorial way of what to do about it.

Senator Mark Warner of Virginia, who had wanted a White House meeting today initially, is now approaching this in a more nuanced way.

His colleagues felt that was not the best approach.

So, instead, they're sort of drawing together, speaking to the White House more in private about their concerns.

Those are things that I think help the president, that they're not being so openly confrontational.

But as opposed to the White House polls that Laura's hearing about, I'm hearing from Democrats about internal polls saying things are not looking good in New Mexico, not in Minnesota, not in Virginia.

They're concerned about those things.

They're not just concerned about losing the White House here, Geoff, but also about the House and Senate, the idea of a Republican takeover of all of government with the favorable Supreme Court.

One senator who is not prone to throwing bombs or having flourishes told me this astounding quote.

That senator said they all campaign, and in this case, everyone can see when a campaign is sort of falling behind, is just kind of in a death spiral.

GEOFF BENNETT: Laura, there is another candidate in this race who has not gotten much attention over these last two weeks, and that's Donald Trump.

He is trying to distance himself from this Project 2025, which you have told us about before, just as Democrats are doing more to try to link him to it.

This is a controversial governance plan if he is elected.

Tell us more about what's happening here.

LAURA BARRON-LOPEZ: That's right.

Former President Donald Trump is essentially saying that he knows nothing about Project 2025, that he doesn't know who's behind it.

But, Geoff, multiple authors of Project 2025 worked in Donald Trump's White House, and they're expected to potentially work in a second Donald Trump White House if he were to win reelection.

This specifically, Project 2025, the blueprint about giving the presidency more power in a Republican White House, as well as gutting federal agencies, restricting abortion across the board, those are things that Biden's campaign really believes that is going to help President Biden strike that contrast.

They see that it's -- that voters are actually starting to take stock of it, that voters are paying more attention to this blueprint, that they do see it as being connected to former President Donald Trump, and so ultimately, you're going to see more from President Biden's campaign playing ads about this, as well as they think it's going to be the way to keep voters on President Biden's side, even in the aftermath of this debate.

GEOFF BENNETT: That is Laura Barron-Lopez and Lisa Desjardins.

Our thanks to you both.