Mr. Obama provided conservatives with not just a health law to loathe and a veto pen to blame, but also a visage that allowed their opposition to be more palpable.
“With Obama no longer being there, the emotional element of the opposition is drained away,” said Rich Lowry, the editor of the conservative National Review.
Republicans also have to contend with an outsider president who never had much of an affinity or loyalty for their party, and who, as a novice politician, has not built the relationships in Washington that are usually needed to get big deals done.
“There’s this disjunction,” Mr. Lowry added. “He doesn’t have a congressional party. He doesn’t even really have a wing of a congressional party.”
In the health care fight, it was not just the far right, egged on by rabble-rousing outside groups, that split from the Republican leadership. There were dissenters among the more middle-of-the-road conservative lawmakers, those representing suburban communities outside Philadelphia and Washington and rural states like Louisiana. Even party leaders like Representative Rodney Frelinghuysen of New Jersey, the powerful chairman of the House Appropriations Committee, opposed the bill.
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.
“Trump, whatever else he is, was able to see that what was being offered to Republicans was not really what they wanted,” said David Frum, the conservative writer and a former speechwriter for President George W. Bush. “They wanted more health care for themselves, less immigration and no more Bushes. And what they were offered was no more health care, more immigration and a third Bush.”
The Trump administration wants to focus next on a tax overhaul. And on that Mr. Trump will probably find agreement with the Republicans in Congress.
But crafting a plan that pleases most conservatives will not be simple. They remain split on some crucial details, like taxing imports. Some in the party, like Mr. Ryan, have favored such a plan, while others, like the Koch-backed political advocacy groups, argue that it could set off trade wars and drive up manufacturing costs.
Speaking to the dismay among many on the right after the health care fight, Ann Coulter, the writer and pundit, attacked Mr. Ryan for pursuing “standard G.O.P. corporatist stuff.”
“What made Donald Trump stand apart from the crowd, and apart from the crowd from every presidential candidate for 20 years,” she said, “was immigration, trade, infrastructure, building a wall. Obviously, that was very, very popular.”
As for Mr. Trump’s Twitter post on Saturday, a White House official said that it and Ms. Pirro’s attack on Mr. Ryan were a coincidence, but the president has been pressed by some advisers to consider Mr. Ryan’s role in the health care defeat.
How Republicans resolve issues of debt and deficit spending also loom as tripwires to the kind of legislative progress Mr. Trump craves — especially after a rocky start to his presidency. These issues, which Mr. Ryan and many other Republicans have been waiting eagerly to tackle since they took power, are not especially important to Mr. Trump, who is more focused on the kinds of projects that are natural to him as a developer, like infrastructure.
And esoteric debates over deficit spending will not matter nearly as much to voters as how their personal finances look.
“When he goes back to Rochester in a re-election campaign, he can’t talk about what’s changed in the deficit — no one will care,” said Frank Cannon, a longtime conservative activist. “But if he can talk about labor rate participation, jobs, jobs that are paying more, that’s what he’ll be judged on. And that’s what Republicans are going to live and die by in the next election cycles as long as he’s president of the United States.”
Because of an editing error, an earlier version of this article twice misstated the day President Trump posted on Twitter about Jeanine Pirro’s show on Fox News. It was Saturday, not Friday or Sunday.
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