Interest groups on the right were also divided, with natural allies like Americans for Tax Reform, the anti-tax outfit, and Americans for Prosperity, a free-market group backed by the Koch brothers, on opposing sides.

While Republicans often said they would deliver freedom and good fortune if given their turn at the wheel, they are now jolted by the realization that their struggles to reach a consensus have thrown into doubt whether they can reach deals on other priorities like a tax overhaul, infrastructure, trade and immigration.

“It is a challenge for the modern Republican Party and the Trump administration to figure out how to get to 218 on a regular basis,” said Grover Norquist, the president of Americans for Tax Reform, who supported the Republican health care bill that failed last week. Generally, 218 is the number of votes needed to pass legislation in the House.

Mr. Norquist said the desire for sweeping change had distorted some conservatives’ perceptions about what could be achieved and how quickly. “They want to change the rules,” he added. “But until you actually change the rules, they’re there, and you have to live by them.”

In a sign of just how deeply this episode has shaken the conservative faction of the party, one of the Freedom Caucus’s members resigned in protest on Sunday, saying he no longer believed the group was effective.

“Saying no is easy, leading is hard, but that is what we were elected to do,” said the lawmaker, Representative Ted Poe of Texas.

What makes progress on any issue so complicated is the fundamental clash between the belief systems of Mr. Trump, whose instincts are more populist than conservative, and Republican leaders in Congress, who are more oriented toward a small-government, free-market policy vision.