It was easy enough for Republicans to rail against the Affordable Care Act when President Barack Obama was in office. There was no political cost to voting, approximately 60 times, to repeal the controversial health-care law, because there was no chance they would succeed, and no chance they would need to craft a replacement plan of their own.

Now, however, the political calculus has changed. Republicans control both houses of Congress, and the White House. After vowing for seven years to dismantle Obamacare, they must deliver.

It’s a familiar quandary for Democrats, who labored for years to devise legislation to increase health insurance coverage, and who spent years afterward suffering the consequences. Ironically, with Democrats out of power, Obamacare is more popular than ever. And Republicans, who leveraged voters’ anxieties over losing their health care plans to seize control of the House in 2010, now risk being undone for the same reason.

It is worth considering how we got here. Emboldened by Donald Trump’s shock electoral win in November, the Republican Party swiftly set in motion the process of repealing Obamacare through a process known as “budget reconciliation,” which would allow the party to gut the law with a single party-line vote. But fissures quickly emerged within the party as public opinion shifted against the G.O.P.’s original plan to repeal the A.C.A. without a ready replacement.

One Nation, a political advocacy group with ties to Senate Majority Leader Mitch McConnell has been circulating a poll on Capitol Hill that shows only 17 percent of people surveyed in potential battleground Senate states believe the law should be repealed immediately, while 34 percent think the party should wait to rally around a replacement. At the same time, approval ratings for the current health system—including, notably, the Medicaid expansion—have reached an all-time high. According to a recent poll by the Kaiser Family Foundation, 84 percent of Americans—and 69 percent of Republican voters—are in favor of the Medicaid expansion, through which an estimated 12 million Americans have gained coverage. A number of Republican governors and senators have recently come to the program’s defense, spurred on by massive, grassroots support among Democrats and Republicans alike.

Recognizing the importance of having an alternative in place, McConnell and Speaker of the House Paul Ryan are currently pushing for a repeal bill that would include a number of replacement provisions—a stopgap that would keep the $3 trillion health care system in serviceable condition until further reforms could be made. The problem is that no one can agree on what the G.O.P. replacement should look like. The party is split between Trump, who has suggested that nobody will lose their coverage under his plan; moderate Republicans, who hope to keep much of the A.C.A. infrastructure in place, but replace elements with more conservative incentives; and more ideological conservatives who don’t believe in government redistribution and say not everyone deserves to receive health care.

Even within the moderate camp, there is vast disagreement. The most popular components of Obamacare are also expensive, particularly the provision barring insurance companies from refusing coverage for people with preexisting conditions, and the G.O.P. can’t decide how to pay for them. “Republicans never ever agree on health care,” former Speaker of the House John Boehner explained during a health-care conference last week, arguing that lawmakers were more likely to simply “fix the flaws and put a more conservative box around it.”

Obamacare “repeal and replace,” Boehner concluded, is “not going to happen.”

Either way, Republicans need Trump, and are looking to him for leadership. “The president’s going to be very pivotal in this,” Representative Dennis Ross of Florida, senior deputy majority whip, told The Wall Street Journal. “He’s got to go into these districts and give air cover to these members who are weak-kneed on some of these issues.” On Monday, Ryan and McConnell are reportedly expected to urge the president to publicly throw his support behind a House G.O.P. plan currently circulating on Capitol Hill and making the rounds in the media. “This is a critical moment for him to get behind this,” one senior congressional aide told CNN.