For President Donald Trump, the failure of the G.O.P.-driven American Health Care Act was a significant policy setback.

WASHINGTON — The effort to end Obamacare is not over, although whether the Affordable Care Act will be completely shelved or recast is unclear.

Despite last month’s aborted House vote on a replacement bill, Republicans continue to seek an alternative to the ACA that the whole party — and possibly some Democrats — can get behind.

“I think it’s time for our folks to come together, and I also think it’s time to potentially get a few moderate Democrats on board as well,” said White House chief of staff Reince Priebus.

To make sure Democrats would negotiate new legislation, President Donald Trump threatened to hold back payments to health insurers approved by President Barack Obama.

“Obamacare is dead next month if it doesn’t get that money,” Trump told The Wall Street Journal in mid-April. “I haven’t made my viewpoint clear yet. I don’t want people to get hurt. … What I think should happen and will happen is the Democrats will start calling me and negotiating.”

On the Republican side, Rep. Mark Meadows of North Carolina, the chairman of the conservative Freedom Caucus, whose opposition doomed the attempted vote in March, proposed leaving in place the existing law’s mandates for insurers to cover people with pre-existing conditions.

Meadows was in frequent talks this month with House Speaker Paul Ryan (R., Wis.), vice president Mike Pence and Rep. Tom MacArthur (R., N.J.), cochairman of the moderate Tuesday Group of House Republicans, to come up with a consensus plan. He said they were nearing an agreement.

White House press secretary Sean Spicer said that “we are getting closer and closer every day” to a consensus, calling Meadows’ input “very helpful,” and saying the Trump administration feels “very buoyed by the direction that this is going.”

A stumbling block may be the administration’s expressed willingness to continue paying subsidies to health insurers under the ACA, even though House Republicans had denounced the payments as illegal and filed a lawsuit in 2014 to end them. A federal district court judge ruled in favor of the legislators, but her decision was stayed pending an appeal filed by the Obama administration.

Under the ACA, insurers are required to reduce deductibles and other out-of-pocket costs for low-income consumers, and in compensation they receive cost-sharing subsidies, totaling $7 billion in all, from the federal government. This year 7 million people, or 58% of all people selecting health insurance plans through the ACA marketplace, qualified for the subsidies.

Two key Republican congressmen — Tom Cole of Oklahoma, chairman of the House Appropriations subcommittee responsible for health spending, and Greg Walden of Oregon, chairman of the Energy and Commerce Committee — have said Congress should appropriate money to fund the subsidies, warning that not doing so could accelerate the exodus of insurers from the program. But the Freedom Caucus is unlikely to agree.

Ongoing payment of the subsidies may depend on whether the administration continues the appeal filed by its predecessor. If President Trump, or his attorney general, Jeff Sessions, decides to drop the appeal, insurers and millions of consumers will lose their subsidies.

Ironically, with scrutiny focused on the contents of the failed American Health Care Act, public opinion of Obama­care improved. A Gallup poll found that the ACA received approval from a majority of those surveyed for the first time, although Republican voters remained overwhelmingly opposed to it.

The AHCA was unveiled by Ryan in early March with strong support from Trump. However, after the nonpartisan Congressional Budget Office estimated that 24 million Americans could lose their health care coverage over the next 10 years under its terms, public criticism began to mount while the Republican congressional majority began to fracture, in part along ideological lines.

On one hand, the Freedom Caucus rejected the bill for not going far enough in abolishing all the provisions of Obamacare. When Republican congressional leaders complied with hard-liners’ insistence on removing federal mandates for minimum benefits, including maternity care and mental health services, a number of moderate Republicans revolted.

Although the president insisted that the bill be brought to the floor for a vote on March 24, Ryan told Trump he lacked the 215 votes needed to pass it and the two agreed to shelve it.

For Trump, who came into office promising “insurance for everybody” and “much lower deductibles,” it was an embarrassing outcome. A Reuters/Ipsos poll conducted March 25 to March 28 showed that, overall, nearly 25% of those surveyed blamed Trump for the failure, but among the Republicans polled few (13%) fixed the blame on the president, instead targeting House Democrats (26%) and House Republicans (23%) as the villains.

“It is a major failure that a high priority of President Trump and the congressional Republican leadership leads to no bill, and the bill as proposed becomes unpopular even among their own voters,” Robert Blendon, a professor at the Harvard T.H. Chan School of Public Health, told The Washington Post. “It’s a real leadership crisis issue.”

Asked if Democrats would work with the administration on another health care bill, Senate Minority Leader Chuck Schumer (D., N.Y.) said, “If they take repeal off the table, ­absolutely.”