The public outbursts are mirrored by internal tensions. With the embers of the old rivalry extinguished between his chief strategist, Stephen K. Bannon, and chief of staff, Reince Priebus, a new realignment has emerged in a West Wing already rived by suspicion and intrigue.

Gary Cohn, the former Goldman Sachs executive who serves as the president’s top economic policy adviser and who is decidedly more liberal than the rest of Mr. Trump’s inner circle, is on the rise, and has the ear of the president’s powerful son-in-law, Jared Kushner. Mr. Kushner also gained an ally on the National Security Council with the appointment of Dina Powell, a Republican and another former Goldman official who worked with Mr. Cohn, as a deputy for strategy…

But in Washington, some Republican lawmakers and officials have watched in dismay and frustration, they say privately, because the president they are looking to for cover and salesmanship of the health care overhaul keeps getting sidetracked…

For Mr. Trump, this was supposed to be a week of pivoting and message discipline. The president read from a script during public appearances and posted on Twitter less often. He invited lawmakers from both parties to the White House for strategy sessions on the health measure. He scheduled policy speeches, like one near Detroit, where he announced that he was halting fuel economy standards imposed by Mr. Obama, and the rally in Nashville, where he visited the grave of Andrew Jackson, the populist patron selected by his history-minded political impresario, Mr. Bannon, as Mr. Trump’s presidential analog.