For months before the first debate, the nation’s voters repeatedly expressed doubts over whether President Biden had the cognitive health enough to serve. 

Today, those doubts have grown even more: now at nearly three-quarters of the electorate, and now including many within his own party.

And today, after the debate with former President Trump, an increased number of voters, including many Democrats, don’t think Mr. Biden should be running for president at all. Nearly half his party doesn’t think he should now be the nominee.

(Trump, for his part, does better, but still only gets half the electorate thinking he has the cognitive health to serve.)

The move came across the partisan board, but it includes a double-digit movement among Democrats, and movement among independents.

Given that, today nearly three in four voters also don’t think Mr. Biden should be running for president in the first place. That’s a higher-percentage sentiment than in February, when almost two-thirds said he should not run.

Most voters who say he shouldn’t run say it’s both about his campaigning and his effectiveness in office, along with his age.

But Democrats’ concerns, when expressed, lean more toward the strategic. They are worried more about his ability to campaign than his decision-making as president.

Trump, by contrast, finds a wide view among Republicans that he should be running. 

That comes as voters widely believe that in the debate, Trump presented his ideas more clearly, appeared more presidential, inspired more confidence, explained his policies better and —quite simply — won the debate. 

This is the case, despite the fact that voters overall think Trump was not as truthful.

And it’s relative, of course. There are plenty of voters who think neither candidate did well.

These views are very similar whether people watched the debate live or just watched highlights or coverage about it, which may speak more generally to the way people get and process information in the modern era.

And Mr. Biden has made no meaningful inroads on convincing voters that a second term would make them financially better off: Trump still is seen as better on this measure.

Nor has Mr. Biden cast himself as better than Donald Trump at protecting democracy.

What now?

After the debate, some Democratic officials reportedly said Joe Biden should step aside as the nominee and give another Democrat a chance to run for president in 2024.

That idea finds resonance with nearly half the nation’s rank-and-file Democrats. 

That’s related to perceptions of Mr. Biden’s health: Democrats who don’t think Mr. Biden has the mental and cognitive health to serve are more likely to say he shouldn’t be the nominee.

And that former number has increased among Democrats. (It’s also gone up among independents.)

The debate has brought the presidential race front and center to the minds of registered voters. Now 59% of registered voters say they are thinking a lot about the presidential race, up from 48% just a few days ago. Interest has risen among Democrats and Republicans alike.

This CBS News/YouGov survey is based on a national sample of 1,130 registered voters who were contacted between June 28-29, 2024. All respondents participated in an earlier national survey of 1,881 registered voters fielded June 17-21, 2024. The sample was weighted by gender, age, race, and education, based on the U.S. Census American Community Survey and Current Population Survey, as well as past vote and partisan identification and weighted to account for differential response rates. The margin of error for the sample of registered voters is ±4.2  points.