In follow-up interviews with half a dozen mainly Republican respondents, none said the president’s coronavirus diagnosis was affecting their voting decision. But some said the debate did affect the way they were thinking about the election, with all but one using the word “bully” to describe the president.

Voters disapproved of the president’s conduct in the debate by a margin of 65 percent to 25 percent. More than half of voters said they strongly disapproved of his conduct.

“I think that Donald Trump acted like a big bully on the stage,” said Cindy Von Waldner, 63, a lifelong Republican from Titusville, Fla. The president began to lose her support when the pandemic hit, and she said she did not believe he took it seriously enough or was transparent enough with the American people. She said she would most likely vote for Mr. Biden, her first time casting a Democratic ballot.

The revulsion against Mr. Trump’s performance extended well into his reliable base. One-third of the president’s supporters said they disapproved of his performance, including 11 percent who did so strongly. A modest but potentially significant 8 percent of people who backed him in the survey said the debate made them less likely to support Mr. Trump’s candidacy.