He told one adviser late Friday that his loss — a legislative debacle foreshadowed by the intraparty fight that led to the 2013 government shutdown — was a minor bump in the road and that the White House would recover.

But his advisers were more realistic. Mr. Trump’s chief strategist, Stephen K. Bannon, according to people familiar with White House discussions, described what happened as a flat-out failure that could inflict serious damage on this presidency — even if Mr. Bannon believes Congress, and not Mr. Trump, deserves much of the blame.

Mr. Bannon and the president’s more soft-spoken legislative affairs director, Marc Short, pushed Mr. Trump hard to insist on a public vote, as a way to identify, shame and pressure “no” voters who were killing their last, best chance to unravel the health care law.

One Hill Republican aide who was involved in the last-minute negotiations said that Mr. Bannon and Mr. Short were seeking to compile an enemies list. But Mr. Ryan repeatedly counseled the president to avoid seeking vengeance — at least until he has passed spending bills and a debt-ceiling increase needed to keep the government running.