A CBS/YouGov poll conducted just after President Biden's debate with Donald Trump, which many even in his own party considered to be a debacle, show that just over half of Democratic registered voters want him to remain the nominee.
Just 27% of registered voters believe he has the mental and cognitive health to serve as President, as opposed to 49% who believe Donald Trump does. Just 28% of registered voters believe he should be running for President, and just 54% of Democratic registered voters believe the same.
Just 55% of Democratic registered voters believe he should continue running, and 45% want him to drop out.
Ultimately, the decision of whether Biden continues on to run for reelection is entirely in his hands, as he has secured the overwhelming majority of delegates to be nominated at his party convention.