WASHINGTON — In his daily briefings on the coronavirus, President Trump has brandished all the familiar tools in his rhetorical arsenal: belittling Democratic governors, demonizing the media, trading in innuendo and bulldozing over the guidance of experts.

It’s the kind of performance the president relishes, but one that has his advisers and Republican allies worried.

As unemployment soars and the death toll skyrockets, and new polls show support for the president’s handling of the crisis sagging, White House allies and Republican lawmakers increasingly believe the briefings are hurting the president more than helping him. Many view the sessions as a kind of original sin from which all of his missteps flow, once he gets through his prepared script and turns to his preferred style of extemporaneous bluster and invective.

Mr. Trump “sometimes drowns out his own message,” said Senator Lindsey Graham of South Carolina, who has become one of the president’s informal counselors and told him “a once-a-week show” could be more effective. Representative Susan Brooks of Indiana said “they’re going on too long.” Senator Shelley Moore Capito of West Virginia said the briefings were “going off the rails a little bit” and suggested that he should “let the health professionals guide where we’re going to go.”

Even the conservative Wall Street Journal editorial board chastised the president for his behavior at the briefings. “Covid-19 isn’t shifty Schiff,” it wrote in an editorial on Thursday, using Mr. Trump’s nickname for Representative Adam Schiff. “It’s a once-a-century threat to American life and livelihood.”

With only intermittent attempts to adapt to a moment of crisis, Mr. Trump is effectively wagering that he can win re-election in the midst of a national emergency on a platform of polarization.

In interviews, Republican lawmakers, administration officials and members of his re-election campaign said they wanted Mr. Trump to limit his error-filled appearances at the West Wing briefings and move more aggressively to prepare for the looming recession. Some even suggested he summon a broader range of the country’s leaders, including former Presidents George W. Bush and Barack Obama, in an all-hands-on-deck moment to respond to the national emergency.

The consternation reflects a new sense of urgency over Mr. Trump’s re-election efforts as Joseph R. Biden Jr. emerges as his likely Democratic challenger. Three new polls this week show Mr. Biden leading the president, and the Trump campaign’s internal surveys show he has mostly lost the initial bump he received early in the crisis, according to three people briefed on the numbers. Public polls show he badly trails the nation’s governors and his own medical experts in terms of whom Americans trust most for guidance.

“I told him your opponent is no longer Joe Biden — it’s this virus,” Mr. Graham said.

One of Mr. Trump’s top political advisers, speaking on the condition of anonymity so as not to anger the president, was even blunter, arguing that the White House was handing Mr. Biden ammunition each night by sending the president out to the cameras.

Vice President Mike Pence, this adviser said, should be the M.C. because he projects more empathy than the president, rarely makes mistakes and, as a former governor and the chief of the coronavirus task force, has a better grasp on the details of the response.

Yet the publicity-obsessed president is unlikely to relinquish his grip on the evening sessions: Mr. Trump has told aides he relishes the free television time and boffo ratings that come with his appearances, administration officials say.

He also views it as an opportunity to put forth his version of events and rebut the negative coverage he is receiving, as he showed in a tweet Thursday afternoon. On a day that New York State reported 799 deaths from the coronavirus in a 24-hour period, Mr. Trump’s focus was on himself, and his feuds.

There is some preliminary evidence that Mr. Trump is heeding the Republicans’ concerns. On Wednesday and Thursday, Mr. Trump made what were for him relatively brief appearances before leaving the room and turning the podium over to Mr. Pence and Drs. Anthony S. Fauci and Deborah Birx. Whether it lasts remains to be seen.

Deep divisions remain in the White House and the Republican Party over how quickly to ease social distancing orders and urge Americans to return to school and work. Some who have Mr. Trump’s ear, like Mr. Graham, are urging prudence. But a number of Republican lawmakers and Fox News personalities are lobbying the president to reopen the economy as quickly as possible.

Amid the conflicting advice, the president’s gut instincts and fondness for showmanship have won out, prompting him to frequently contradict or simply obscure the scientists who polls show are most trusted by voters.

And it’s not just an overwhelming majority of voters who believe the medical experts should be center stage: Senator Mitch McConnell, the majority leader, personally urged Mr. Trump at the start of the crisis to let Drs. Fauci and Birx be the face of the response, according to a Republican official familiar with their conversation.

Judd Deere, a White House spokesman, said: “Any suggestion that President Trump is struggling on tone or message is completely false. During these difficult times, Americans are receiving comfort, hope and resources from their president, as well as their local officials, and Americans are responding in unprecedented ways.”

Some of Mr. Trump’s aides have quietly suggested to him that he ratchet back his public attacks on the governors who have emerged as leaders in the response to the virus. But they acknowledge their efforts can be something of a fool’s errand; the president has his style and he won’t change, they say.

His attacks on Gov. Gretchen Whitmer of Michigan, a popular Democrat and potential vice-presidential pick for Mr. Biden — whom Mr. Trump called a “half-Whit” and “that woman” — were of particular concern to some aides and political advisers, who believe he risked alienating voters in a pivotal state.

Representative Paul Mitchell, a Michigan Republican, said he had contacted a senior White House official, as well as Ms. Whitmer herself, to express his unhappiness about their mutual sniping.

“It is not helpful to hurl names and talk about badly about people,” Mr. Mitchell said. “We need to focus on the problem.”

At Mr. Trump’s re-election campaign, staff members have closely monitored internal polling data showing an erosion of the gains Mr. Trump made immediately after he put social distancing guidelines in place. Advisers are torn between knowing that a less abrasive approach would help Mr. Trump and their awareness that he can’t tolerate criticism, regardless of the setting.

Mr. Trump’s limited gains in the polls are all the more striking when compared with those made by governors in both parties; many are enjoying double-digit gains in their approval ratings. And Mr. Trump’s penchant for ad hominem attacks, Republicans say, illustrates why he has little room for growth among the electorate.

“He can’t escape his instincts, his desire to put people down, like Mitt Romney, or to talk about his ratings,” said former Representative Carlos Curbelo, a Florida Republican. “That’s why he’s not getting the George W. Bush post-9/11 treatment. A leader in this sort of crisis should have a 75-to-80-percent approval rating.”

That would prove difficult for even a more conventional president at a time the country is so politically divided, but a number of prominent Republicans believe Mr. Trump has hurt himself by making only the most halting attempts at demonstrating an above-the-fray unity.

For example, aides to both Mr. Bush and Mr. Obama said that neither had been asked by the White House to do anything to aid the response to the crisis.

“The model of Obama asking Bush and Clinton to work on Haiti is a really good model,” said former Gov. Bill Haslam of Tennessee, recalling how Mr. Obama deployed Mr. Bush and former President Bill Clinton to lead the United States’ assistance to Haiti after the devastating 2010 earthquake there.

But Mr. Haslam and other Republicans believe Mr. Trump needs to go much further. Mr. Haslam called for creating a recovery team and installing “the economic equivalent of Dr. Fauci” as its leader. Asked whom he had in mind, Mr. Haslam suggested Mitch Daniels, who previously served as the governor of Indiana, the head of the Office of Management and Budget and as chief executive of the pharmaceutical company Eli Lilly.

A number of senators, including Mr. Graham, are also pushing for a sort of economic task force to complement the virus task force.

“The administration needs to be thinking through what does it look like to get back to business,” said Senator Pat Toomey of Pennsylvania, suggesting that it should “give a lot of thought to how we scale back up economically, because that’s going to be the next big challenge for us.”

The health of the economy may pose the biggest challenge to Mr. Trump’s re-election.

Mr. Toomey said he “won’t be surprised if we have 25 percent unemployment,” which would match the height of the Great Depression, by the start of the summer. But he said that if voters believed “the president has handled this well under the circumstances, and we’re on a good path, he has a shot.”

Other Republicans are more skeptical that Mr. Trump can win if he’s still saddled with double-digit unemployment in November. “I think that makes it really hard,” said Tony Fratto, a former Bush administration official.

And then there’s the matter of Mr. Trump and his conduct at the daily briefings.

Mr. Toomey has been outspoken about the need for Americans to wear masks when they leave home. Last week he had a 20-minute conversation with the president, whom he described as “thoughtful and engaged.”

By week’s end, the Centers for Disease Control and Prevention had issued guidelines: People should wear “cloth face coverings in public settings where other social distancing measures are difficult to maintain.” The agency’s decision was based in part on recent studies showing that people without symptoms can give the virus to others.

But in the same briefing where he announced the guidelines, Mr. Trump diminished the move as “a recommendation.”

“I just don’t want to wear one myself,” he said, explaining that he had no symptoms. “I am feeling good.”