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.”