“People had opinions about this president very early in his administration, and they were strongly held opinions,” Alec Tyson, a senior researcher at the Pew Research Center, said in an interview. “It’s unlikely that people are just developing opinions about Trump now.”

To the degree that Mr. Trump is getting a bump in approval, the Pew poll found that it was coming especially from those who consider themselves political independents but lean Republican. His approval rating has leapt nine percentage points with these Americans since January, when the coronavirus was first detected in the United States. (Disapproval of Mr. Trump also softened slightly among Democrats, though to a lesser degree.)

This group could represent a crucial voting bloc for Mr. Trump in the November general election. As partisan Republicans have coalesced around him, he has struggled among some moderate and conservative voters who don’t feel an allegiance to the party. If former Vice President Joseph R. Biden Jr. secures the Democratic nomination, he is certain to make an aggressive play for many of these voters.

In a sign of how prevalent the virus’s effects already are, more than one in 10 voters in the Fox poll said they knew someone who had been infected. And 43 percent said they or someone in their household had lost work because of the virus, including two-fifths of Republican voters.

Many Americans who might not typically pay close attention to politics may now be looking to Mr. Trump and Congress for a solution. Ninety-five percent of voters said they were following virus-related news at least somewhat closely, the Fox poll found. And as Congress pieced together an enormous $2 trillion stimulus package this week, voters’ approval of Congress reached a 10-year high. At just 31 percent, it’s still dismal — but over the past decade that number has more typically lingered in the teens.

The president’s daily news briefings during the crisis have averaged about 8.5 million viewers on cable news channels, on par with the season finale of “The Bachelor.” Those numbers don’t include the millions of people who are watching on broadcast stations and over the internet.

Mr. Trump is typically flanked at these briefings by government doctors and members of his administration, and his confident, freewheeling style may appeal to certain persuadable voters. But if the death toll skyrockets and the economy stays dormant, Mr. Trump’s hesitancy to take certain broad federal actions could expose him to criticism.