While polling indicates that most Democrats take a sharply negative view of the president and his handling of the virus, and that some Republicans share concerns about Mr. Trump’s performance as well, there are no signs at this point that the epidemic has cut deeply into the bedrock support that he enjoys among his base, even in places where infection rates are high and populations are most at risk.

Lee Green, a 59-year-old who lives in the Florida retirement community of The Villages and leads the Jewish Conservatives Club there, said she typically gets her news from Facebook, where she is subscribed to updates from outlets like The Daily Wire and The Jerusalem Post. But on Wednesday she struggled to understand why, if the virus was indeed the equivalent of a “bad flu,” schools were closing and events were being canceled.

Now, she relies on the C.D.C. website for updates. “I don’t see them as political hacks,” she explained.

Ms. Green is confident in the C.D.C., in large part because she believes Mr. Trump is, too. Later in the week, after the president declared a national emergency over the pandemic, her confidence that Mr. Trump was leaning on experts to do what was best for Americans had only soared.

“I’m actually even more impressed after today’s press briefing,” she said on Friday, after the president spoke in the Rose Garden, with top health officials and C.E.O.s. “I voted for Trump because he’s a problem solver. And initially he wanted to be super optimistic about everything, but when the experts told him this was a really big deal, he instantly took action.”