Welcome to Poll Watch, our weekly look at polling data and survey research on the candidates, voters and issues that will shape the 2020 election.

The Trump administration is engaged in a not-so-quiet whisper campaign to cast doubt on Dr. Anthony S. Fauci, the country’s top infectious disease expert, and other public health officials.

President Trump’s team has increasingly questioned Dr. Fauci’s track record, and this week the White House moved to strip the Centers for Disease Control and Prevention of control over collection of data on the coronavirus’s spread.

All of this lines up with Mr. Trump’s attempts to speed up the reopening process, often in spite of his health advisers’ warnings. Presumably, Mr. Trump is playing the long game, hoping that a return to normal will bring the economy booming back in time for the November election and that the virus could either “fade away” or become preventable by a vaccine.

But none of those things have happened so far, and when it comes to public opinion, the president appears to have boxed himself into a corner.

After tapering down throughout most of the spring, cases have been rising steadily for the past month, giving pollsters enough time to take a read on how Americans have responded to the virus’s resurgence.

Most people continue to prefer a cautious reopening, and they increasingly disapprove of Mr. Trump’s handling of the pandemic. When it comes to the health experts he’s been vilifying, people’s faith has hardly been shaken.

Voters over all (but no longer Republicans) have faith in Fauci.

As Mr. Trump and his allies in the conservative media have sown doubt about Dr. Fauci, many Republicans have in fact turned against the doctor. Back in May, a CNN poll found that by a two-to-one margin, Republicans said they trusted the information Dr. Fauci was providing. But on Wednesday, Quinnipiac University released a poll showing that 52 percent of Republicans now said they did not trust Dr. Fauci on the pandemic. Just 39 percent said they did.

Yet among Democrats and independents, trust in Dr. Fauci had risen, if anything. Eighty-six percent of Democrats and two-thirds of independents told Quinnipiac researchers that they had faith in the information Dr. Fauci provided. Over all, 65 percent of the country continued to say it had faith in Dr. Fauci, according to the poll.

Strikingly, the poll found that Dr. Fauci had the trust of a majority even in some of Mr. Trump’s core demographics: white Americans without college degrees (59 percent), people living in rural areas (55 percent) and white men (61 percent).

The president, meanwhile, was in bad shape here: In each of those groups, fewer than half of respondents said they trusted him to provide information about the virus. It is more evidence that even while Mr. Trump continues to exert command over the Republican Party faithful, his handling of the virus may be driving down support for him — and possibly for the party — among certain must-win demographics.

This has also put down-ballot Republicans in a bind. Caught between Mr. Trump’s calls to reopen and the public’s overwhelming desire to exercise caution, relatively few congressional Republicans who are looking at competitive elections in November have placed the virus at the center of their campaigns. Yet most voters call the pandemic an issue of critical importance to their candidate choice.

Trump’s numbers are down even with core groups.

Even for self-identified Republicans — who continue to express overwhelming approval of Mr. Trump’s performance — confidence in his handling of the pandemic has been shaken. His approval rating specifically on the virus dipped below 80 percent among Republicans in both the Quinnipiac poll and an ABC News/Ipsos poll last week.

Just 51 percent of white voters without a college degree told Quinnipiac interviewers that they approved of his job performance over all, down from 60 percent a month ago. Among white evangelicals, approval of Mr. Trump’s job performance had dropped to 70 percent, a 10-percentage-point drop from a May Quinnipiac poll.

By a 14-point margin, voters said in a CNBC poll last month that they thought Joseph R. Biden Jr., the presumptive Democratic presidential nominee, would do a better job handling the pandemic than Mr. Trump.

Americans are hesitant to reopen schools — and supportive of masks.

With coronavirus cases climbing in most states, Mr. Trump has not articulated a clear national framework for confronting the disease. Virus and antibody tests — which he often calls central to the administration’s strategy — have recently begun to take weeks to produce results in many cases. Even as he presses for schools to reopen, he has declined to issue a national plan for how to do so safely.

On Thursday, the White House press secretary, Kayleigh McEnany, said “science should not stand in the way of” allowing schools to reopen.

But in a poll conducted at the end of last month, Ipsos found that 71 percent of American parents thought it would be risky to send their children back to school. And most parents said that if their state experienced a second wave of the virus in the fall, they would probably keep their children at home.

On the broader question of reopening, the majority of the country remains firmly against Mr. Trump’s aggressive push. Roughly three in five respondents to the ABC/Ipsos poll last week said the country was reopening too quickly; just 15 percent said it was moving too slowly.

A number of states have ordered residents to wear masks in public — including Arkansas and Colorado, which announced mask-wearing mandates on Thursday. Mr. Trump has made his ambivalence about masks well known, but this week’s Quinnipiac poll found that 71 percent of Americans would support a national mandate.

Seventy-three percent said that Mr. Trump himself ought to wear a mask when he’s in public.