That carries over into perceptions of how Mr. Trump has dealt with the coronavirus specifically. And, importantly, it holds true in swing states.

A University of New Hampshire poll released this week had encouraging news for Mr. Trump. While his overall virus approval rating in that state remained underwater, independents’ approval jumped in the past month by 21 percentage points, showing that his message — inconsistent though it may be — is still persuasive for some key voters.

Surveys released this week of Florida, Michigan and Pennsylvania found approval of his handling of the pandemic varying from 44 percent to 46 percent of registered voters in those states, reflective of the national average.

In Michigan and Pennsylvania, Biden doesn’t necessarily benefit from people’s support of Democratic governors.

These new state polls show that even in places where Mr. Trump has clashed with popular Democratic governors, Mr. Biden will not be able to lean on support for state-level Democrats in his fight against the president.

In Fox News polls of Michigan and Pennsylvania, well over three in five voters approved of their Democratic governor’s job performance, including large majorities of independents and moderates. But in each case, that was far more than those who said they would vote for Mr. Biden in November.

And voters appear to see their governor as separate from their vote in the presidential election. In a hypothetical matchup against Mr. Trump, Mr. Biden didn’t do markedly better when Michigan voters were asked about a hypothetical ticket that included their governor, Gretchen Whitmer, as his running mate. In each case, 49 percent said they would vote for Mr. Biden over Mr. Trump.

In Florida, Biden emerges from the primary race looking weakened — but with room to grow.

A Quinnipiac University poll of Florida released on Wednesday showed Mr. Biden with a slight edge among registered voters, but that spread of four percentage points was within the margin of error. Mr. Biden has fallen since June, when he led Mr. Trump, 50 percent to 41 percent.