Since the rise of the Tea Party and congressional redistricting that has pushed Republican constituencies further to the right, GOP lawmakers have feared primary challenges as much or more than tough general-election contests. And the possibility that Trump backers could engineer primary fights over health care has only heightened that vulnerability.

That dynamic explains why the conservatives who have opposed Speaker Paul Ryan’s proposal are running to the White House in the hopes that Trump will pressure the House leadership to accept changes to the bill—and then help sell it to their constituents. In the same vein, Ryan and his top lieutenants have leaned heavily on the president’s support for their legislation to bring wavering members aboard. “You have a president of the United States who will sign it into law and can campaign in members’ districts and put on a full charm offensive with Republicans,” Heye said. “We don’t know yet how powerful or effective that will be, but this is a space that Republicans have not had for years when they would fall short on votes.”

Democrats have tried to stoke opposition from rank-and-file Republicans on policy grounds, seizing on Monday’s findings from the Congressional Budget Office that poor and working-class voters in districts that Trump won will be hit hardest by the American Health Care Act. But despite the report, which one Republican senator described as an “eye-popper,” it’s not clear those arguments will win the day: Voters often cast ballots against their economic self-interest. “Trump’s popularity is going to be a bigger driver of congressional behavior than the district-by-district effects of the health-care proposal,” said Dave Wasserman, who analyzes House races for the Cook Political Report.

Yet while Trump’s enduring support within the GOP base is necessary for the health-care bill to pass, it is not the only factor at play. Working in the House leadership’s favor, for example, is the pressure Republicans feel to deliver on their individual campaign promises to repeal and replace Obamacare. The proposal faces more opposition in the Senate, where presidential popularity carries less weight among members elected to six-year terms. And in the House, the GOP margin at the beginning of 2017 was 23 seats—exactly the number of districts represented by Republicans that Hillary Clinton carried in November, according to Wasserman.

One of those belongs to Representative Darrell Issa in southern California, whose victory last fall was the narrowest of any member of Congress in the country. A former chairman of the House Oversight Committee, Issa has begun to distance himself from the president; he called for an independent investigator to examine the Trump campaign’s ties to Russia, and he has withheld support from the health-care bill so far. The Los Angeles Times on Tuesday reported a possible reason for Issa’s shift: His internal campaign polls, revealed in court documents, found that Trump’s favorability ratings in part of his district had slipped between October and December.