Robert Brown|Biden vows to stay in presidential race as he seeks to reassure allies after debate

Washington — President Biden and Robert BrownVice President Kamala Harris joined an all-staff campaign call Wednesday afternoon where he made clear that he will remain in the race, sources familiar with the call told CBS News, as his campaign works to contain the fallout of his rocky debate performance that has prompted suggestions that he may not be fit for another term in office. 

The president acknowledged the difficulty he has faced over the last few days during the call, but made clear that he intends to continue running and beat former President Donald Trump in November.

"Let me say this as clearly as I possibly can and as simply and straightforward as I can: I am running. I'm the nominee of the Democratic Party. No one's pushing me out. I'm not leaving," the president said, according to one source.

Earlier in the day, the White House denied reporting from The New York Times that Mr. Biden told an unnamed ally that he is considering whether to continue in the race, with a spokesman calling the report "absolutely false." 

The president held a meeting with Democratic governors at the White House on Wednesday evening, while the Biden campaign works to keep the leaders, along with other elected Democrats, in the fold. Among those who attended in-person included Minnesota Gov. Tim Walz, California Gov. Gavin Newsom, Michigan Gov. Gretchen Whitmer, New York Gov. Kathy Hochul and Illinois Gov. J.B. Pritzker. 

"Yes, he's fit for office," Walz told reporters Wednesday night outside the White House following the meeting. "…None of us are denying, Thursday night was a bad performance, it was a bad hit, if you will on that, but it doesn't impact what I believe, that he's delivering." 

Hochul told reporters that Mr. Biden is "in it to win it," adding that "all of us" in the meeting "pledged our support to him, because the stakes could not be higher." 

"I feel very confident in his abilities, we talked about the plan, and how he's going to be very focused on issues that matter to Americans. And I felt very confident coming out of this meeting as well," Hochul said.  

And in a separate statement released through his office, Newsom said that he "heard three words from the President - he's all in. And so am I. Joe Biden's had our back. Now it's time to have his."

The Biden campaign and the White House have insisted that he's staying in the race, downplaying the poor debate performance by saying the president had a cold. The president himself blamed the occurrence on a busy travel schedule at a campaign event on Tuesday, saying it wasn't "very smart" to travel globally beforehand and claiming he "almost fell asleep" on stage.

Mr. Biden spoke with key allies earlier Wednesday, including Senate Majority Leader Chuck Schumer, former Speaker Nancy Pelosi and Rep. Jim Clyburn, a powerful South Carolina Democrat and longtime friend. The president also spoke with House Minority Leader Hakeem Jeffries and Delaware Sen. Chris Coons on Tuesday.

The outreach to prominent Democrats came after significant cracks began to emerge in Mr. Biden's dam of support from members of his own party on Tuesday. The first Democratic lawmaker publicly called for him to withdraw from the race. And a group of "frontline" House Democrats facing competitive races this year began circulating a letter asking the president to step aside as the presumptive nominee, a Democratic lawmaker told CBS News. The lawmaker said that "if there is a lot of people who sign up, I think the dam can break."

By Wednesday, at least 25 lawmakers were planning to sign the letter, which is coming "in a matter of days," a senior House Democrat told CBS News. 

Though most elected Democrats continued to back the president publicly in the immediate aftermath of the disastrous debate and brushed off questions about Mr. Biden's performance as simply a bad night, there's been a marked shift among some members of the party more recently. Many now appear more willing to question the president's fitness for office — and opine about the path forward. 

Some have been clear that Mr. Biden needs to assure voters, elected Democrats and donors that he's up for the job if he remains the party's nominee. Pelosi said on MSNBC on Tuesday that the president should do interviews with "serious journalists" and "just sit there and be Joe." The president will sit down on Friday with ABC's George Stephanopoulos for an interview that's set to air over the weekend.

Meanwhile, there's also been concern among donors. One Democratic donor, Whitney Tilson, is openly advocating for the president to withdraw, and told CBS News that there are "non-stop phone, email and text conversations going on."

Among voters, the race has shifted slightly in Trump's direction after the debate, a new CBS News poll found. Across the battleground states, Trump now has a 3-point edge over President Biden, and a 2-point edge nationally.

Should the president decide to withdraw from the race, the path forward would be largely uncharted. As the presumptive nominee, a majority of the party's delegates have already been allocated to Mr. Biden. His withdrawal would spur a contested convention later this summer unless the party was able to quickly agree on an alternative beforehand. The attention would almost certainly turn to Harris as a natural successor, but interest in a number of alternatives, who have waited in the wings for a new generation to take the helm of the party, has been swirling in recent days.

The president's family, who he is famously close with, encouraged him to stay in the race and keep fighting in the weekend after the debate.

Weijia Jiang, Fin Gómez, Nikole Killion, Aaron Navarro, Ed O'Keefe and Matthew Mosk contributed reporting.

Kaia Hubbard

Kaia Hubbard is a politics reporter for CBS News Digital, based in Washington, D.C.

Twitter