President Trump and Republicans in Washington have shaken the confidence of their supporters after a punishing and self-inflicted series of setbacks that have angered activists, left allies slack-jawed and reopened old fissures on the right.

A seemingly endless sequence of disappointments and blunders has rattled Mr. Trump’s volatile governing coalition, like Mr. Trump’s attacks on Attorney General Jeff Sessions; a vulgar tirade by his new communications chief, Anthony Scaramucci; and the collapse of conservative-backed health care legislation.

Mr. Trump remains overwhelmingly popular with Republicans, but among party loyalists and pro-Trump activists around the country, there are new doubts about the tactics he has employed, the team he has assembled and the fate of the populist, “drain the swamp” agenda he promised to deliver in partnership with a Republican-controlled Congress.

“There is a significant amount of justified frustration, particularly with the Senate,” said Robin Hayes, the chairman of the North Carolina Republican Party, alluding to the health care defeat. “I don’t want to use any Scaramucci language this morning, but it’s their inability to function as a team, to work together and come up with a responsible win.”