“We’re going to try and measure three times and saw once,” Representative Pete Sessions, Republican of Texas and the chairman of the House Rules Committee, said late Thursday. “A lot of people around this town have tried their best to try and rush it, rush it, rush it.”
He urged patience, saying the health bill “will find its time.”
The lost opportunity was perhaps the biggest blow to the future prospects of Reince Priebus, Mr. Trump’s chief of staff, who has a long relationship with Speaker Paul D. Ryan of Wisconsin. Mr. Priebus had pushed aggressively for the House to schedule a vote this week, according to several people who spoke with him within the West Wing and on Capitol Hill.
Earlier on Thursday, Mr. Ryan appeared to shy away from pushing for a fast vote. “We’re going to go when we have the votes,” he said, adding that Republicans would not be constrained by “some artificial deadline.”
House Democrats, sensing an advantage, pressured Republicans to once again back away from the bill, just as they did a month ago in an embarrassing defeat for Mr. Trump and Mr. Ryan. Democratic leaders threatened to withhold votes from a stopgap spending measure to keep the government open past Friday if Republicans insisted on trying to jam the health care bill through the House on Friday or Saturday, which is Mr. Trump’s 100th day as president.
The House Democratic leader, Nancy Pelosi of California, said Mr. Trump was “really making fools of the members of Congress of his own party” by asking them to support a health bill that is unpopular with the public.
“If they vote on it, the minute they cast that vote, they put doo-doo on their shoe,” she said.
Republican leaders in both chambers plan to pass the stopgap measure to give lawmakers another week to work out a spending package to fund the government for the remainder of the fiscal year, which ends Sept. 30.
The longer-term spending deal is expected to provide more funding for the military and for border security, although Mr. Trump backed off his demand that lawmakers provide money for the wall he wants to build along the border with Mexico.
Mr. Ryan brushed off the threat from Democrats. “I would be shocked that they would want to see a government shutdown,” he said.
But Mr. Trump was not so dismissive. He unleashed a torrent of Twitter posts on Thursday accusing Democrats of wanting to shut down the government. The posts accused Democrats of putting the needs of health insurance companies, Puerto Rico and undocumented immigrants over the military, visitors to national parks and coal miners — claims that Democrats called absurd.
The latest House plan to repeal and replace the health law would include an amendment drafted by Representative Tom MacArthur, Republican of New Jersey and a leader of a centrist bloc of lawmakers called the Tuesday Group.
Mr. MacArthur’s amendment would allow states to opt out of certain provisions of the Affordable Care Act, including one that requires insurers to provide a minimum set of health benefits and another that prohibits insurers from charging higher premiums based on a person’s health status.
Republicans say the federal mandates drive up costs, but Democrats say they provide important protections for consumers.
Under Mr. MacArthur’s amendment, states could obtain waivers letting them redefine the “essential health benefits,” which now include maternity care, emergency services, mental health care and drug addiction treatment.
Republicans say their bill maintains protections for people with pre-existing conditions. But Democrats say the waivers would severely weaken these protections because insurers could charge higher premiums to sick people who wanted to buy insurance after a gap in coverage.
Republicans say their bill offers billions of dollars that states could use to operate high-risk pools or other programs to provide or subsidize insurance for people with pre-existing conditions.
The American Medical Association and AARP, the lobby for older Americans, oppose the latest version of the Republicans’ health care bill.
“Although the MacArthur amendment states that the ban on pre-existing conditions remains intact, this assurance may be illusory, as status underwriting could effectively make coverage completely unaffordable to people with pre-existing conditions,” said Dr. James L. Madara, the chief executive of the American Medical Association.
Mr. MacArthur said Thursday that his amendment had won over some of his Republican colleagues, though not enough to pass the bill. “But we are closer today than we’ve ever been,” he said. “We’re getting there.”
At the same time, his amendment highlighted the gulf between hard-line conservatives and more moderate Republicans when it comes to how to go about repealing and replacing the Affordable Care Act.
For the Freedom Caucus, which shouldered much of the blame for the House bill’s failure last month, the amendment functioned as a way to shift any finger-pointing to a different bloc of members.
But the latest version of the House bill seemed to offer little that would entice anyone with reservations other than the hard-line conservatives.
“The proposed changes to this bill would leave too many of my constituents with pre-existing conditions paying more for health insurance coverage, and too many of them will even be left without any coverage at all,” Representative Ileana Ros-Lehtinen, Republican of Florida, said Thursday.
It also gave pause to some Republicans who were ready to vote in favor of the measure last month.
Representative Mario Diaz-Balart, Republican of Florida, planned to support the bill last month before it was pulled. But on Thursday, he acknowledged “a lot of red flags,” including what would happen to people with pre-existing conditions. “How are they treated?” he asked. “What options do they have?”
The House plan had already faced deep skepticism in the Senate, where other policy concerns are certain to be debated, like the future of Medicaid in states that expanded eligibility under the Affordable Care Act.
The Senate Democratic leader, Chuck Schumer of New York, argued on Thursday that the core of Mr. MacArthur’s amendment would violate the budget rules that Republicans must follow in order to sidestep a Democratic filibuster.
Mr. Schumer warned House Republicans against voting for a flawed bill “to save face for the president in the first 100 days.”
“Why,” he asked, “would you risk voting yes for a bill that is devastating to your constituents and has no chance of becoming law?”