Mr. Trump has told four people close to him that he regrets going along with Speaker Paul D. Ryan’s plan to push a health care overhaul before unveiling a tax cut proposal more politically palatable to Republicans.

He said ruefully this week that he should have done tax reform first when it became clear that the quick-hit health care victory he had hoped for was not going to materialize on Thursday, the seventh anniversary of the act’s passage, when the legislation was scheduled for a vote.

Two of his most influential advisers — Stephen K. Bannon, his chief strategist, and Gary D. Cohn, the National Economic Council director, who had a major role in pushing the bill — came to agree, and did not like the compromise that was emerging. So on Thursday night, Mr. Trump delivered an ultimatum.