But Democrats were not in a negotiating mood, at least on Friday, soured by how a seeming alignment with Mr. Trump on the immigration issue was ruptured by subsequent White House demands for money for the president’s wall on the southern border with Mexico and other hard-line policies as trade-offs. They expressed more anger over the Mr. Trump’s health care actions, seeing them as deliberate efforts to sabotage the system to get Democrats to the table.

“What brings us to the table is trying to do some good for people,” said Senator Chuck Schumer, Democrat of New York and the minority leader. “But as in the past, threats and bullying is not going to work. In this, politically, he’s in much worse shape than we are. The American people, even a large number of Republicans, are on our side in terms of improving the system, not destroying it. And so I don’t think he has much leverage to threaten or bully.”

William A. Galston, a former White House domestic policy aide to President Bill Clinton, said Democrats were unlikely to respond to Mr. Trump’s pressure tactic. “It’s equivalent to hitting a mule over the head with a two-by-four and then expecting it to nuzzle up to you,” he said. “In the current climate, it’s difficult for me to believe that Democrats are going to come running to Trump and say, ‘O.K., let’s negotiate now on health care.’ I just don’t see that happening.”

In forcing the issue on health care, Mr. Trump may have scuttled bipartisan talks already underway about legislation intended to stabilize the insurance markets under Mr. Obama’s Affordable Care Act. He also scrambled the congressional agenda at a time when lawmakers face several big tests in coming weeks.

Congress is already struggling to restore funding for a children’s health care program that expired, and it faces a Dec. 8 deadline to finance government operations across the board. The immigration program will expire in the new year without action, and at some point around then lawmakers will have to increase the debt ceiling or face default.

Mr. Trump also faces obstacles to pushing through his major tax cut program by the end of the year. And his Iran decision on Friday starts a 60-day clock for lawmakers to consider reimposing sanctions on Tehran, a move that would effectively blow up the nuclear agreement.

Aides to the president said there was no concerted effort to use executive power all at once to move his agenda forward, and that each decision was driven by separate timetables, some of them according to various legal calendars. But they also noted that Congress in recent years has demonstrated that it rarely takes difficult decisions unless it faces deadlines with dire consequences for inaction, such as a government shutdown.