AMNA NAWAZ: The weekend did little to settle concerns inside the Democratic Party after President Biden's widely panned debate performance.

Questions about whether the president should step aside have only intensified.

JOE BIDEN, President of the United States: But here's the deal.

AMNA NAWAZ: The debate over the debate continues.

REP. JAMIE RASKIN (D-MD): There are very honest and serious and rigorous conversations taking place at every level of our party.

AMNA NAWAZ: President Biden's allies have flooded the airwaves... SEN. CHRIS COONS (D-DE): The only Democrat who's ever beaten Donald Trump is Joe Biden.

He is our candidate for November and he has the best shot to beat him.

AMNA NAWAZ: ... to defend his place as the Democratic Party nominee.

SEN. RAPHAEL WARNOCK (D-GA): The question this morning is not, what is Joe Biden going to do?

The question is, who has Donald Trump ever shown up for, other than himself and people like himself?

I'm with Joe Biden and it's our assignment to make sure that he gets over the finish line come November.

AMNA NAWAZ: But behind closed doors, the party is in panic, with many Democrats suggesting the president should drop out of the race before the party's convention next month to give the delegates the opportunity to nominate someone else.

And there are several potential replacement names being mentioned, including some high-profile governors, Josh Shapiro of Pennsylvania, Gavin Newsom of California, and Gretchen Whitmer of Michigan.

Whitmer reportedly called the Biden campaign, distancing herself from the rumors, but delivering a stark warning: Winning Michigan is out of reach in November.

Democratic voters are equally split on what Mr. Biden should do.

In a CBS News/YouGov poll, 55 percent of Democrats say the president should keep running, but 45 percent say he should step aside.

The concerns have even reached the world stage.

Secretary of State Antony Blinken was asked how U.S. allies responded.

ANTONY BLINKEN, U.S. Secretary of State: What the world knows, the world has experienced over 3.5 years, not one night, is exactly the kind of leadership that he's brought to bear.

AMNA NAWAZ: The president remains committed to the fight for now after huddling with his family yesterday at Camp David, first lady Jill Biden and his son Hunter among those urging him to stay in the race.

JOE BIDEN: The most lies told in the single debate.

AMNA NAWAZ: His campaign also launched a new ad, taking aim at Donald Trump's own debate performance and record as president, and using Biden's fiery speech at a rally in North Carolina to make the case for his continuing campaign.

JOE BIDEN: When you get knocked down, you get back up!

(CHEERING AND APPLAUSE)