WASHINGTON—President Donald Trump on Tuesday put his political capital on the line in a late effort to save the House Republican legislation that aims to replace the Affordable Care Act, but he didn’t immediately win over the conservative holdouts who could scuttle the bill.

Mr. Trump traveled to Capitol Hill and delivered a warning to House Republicans that they would lose seats in 2018 if they didn’t follow through on their promise to repeal former President Barack Obama’s health law.

In a closed-door meeting of GOP members, Mr. Trump singled out the leader of the conservative House Freedom Caucus, Rep. Mark Meadows (R., N.C.), and cautioned him to drop his opposition to the bill.

“At the end, I think Mark’s going to be with me, right?’’ Rep. Fred Upton (R., Mich.) recounted Mr. Trump as saying.

Some lawmakers added that Mr. Trump said he would make life uncomfortable for Mr. Meadows if he didn’t change his stance, a comment that some took to be in jest and others as more threatening.

Several lawmakers said the president told the group: “I’m afraid you’re going to blow it.’’

Mr. Meadows, whose bloc claims it has enough votes to defeat the bill, said he wasn’t convinced by Mr. Trump—a sign GOP leaders have more work to do to secure the votes needed to pass the bill.

“It won’t lower premiums, and until it does, I’m going to be a ‘no,’ even if it sends me home,” Mr. Meadows said of the legislation after the president addressed lawmakers.

“As a person, I love him,” said Rep. Rod Blum (R., Iowa), after the president’s presentation. Hearing from Mr. Trump “was a lot of fun. But it didn’t change me at all.”

Some House Republicans privately said Mr. Trump’s lobbying for the bill would make it harder for conservatives to vote against the legislation. All House Democrats are expected to oppose the bill. The full House is expected to vote on the legislation on Thursday.

The high-pressure sales pitch has underscored the stakes for Mr. Trump and House Republican leaders, who have said they need to act quickly to move on to other important issues, such as an overhaul of tax policy.

A senior White House official said Tuesday that the administration had been disappointed by the decision of some conservative groups to withhold support from the bill, but had secured other important conservative endorsements on Tuesday.

Mr. Trump met later in the day with a group of centrist Republican House members, some of whom remain undecided, while others lean against the bill. The centrists discussed their desire to boost financial support to older Americans, as well as other issues important to their districts, the official said.

On Tuesday night, Messrs. Ryan and Trump repeated their pitch at a fundraising dinner for House Republicans. Mr. Ryan told the crowd that “on Thursday, we should go out and deliver on our promise” and he hoped everyone would “stand with President Trump.”

Mr. Trump said the elections had given the party “clear instructions” and “that legislative effort begins with Thursday’s crucial vote” on the health bill.

House leaders sought to satisfy conservatives Monday with changes to the bill, including an optional work requirement for certain Medicaid beneficiaries.

But some members of the Freedom Caucus, which met to discuss the legislation on Tuesday after Mr. Trump’s pitch, want a speedier phaseout of the Medicaid expansion that took place under the ACA. They also want to strip the bill of a new set of tax credits to help people buy insurance if they don’t get it at work.

Senate Minority Leader Chuck Schumer (D., N.Y.), addressing those late changes, said he was concerned about the number of Americans who would lose health insurance. “The changes they announced last night amount to a fresh coat of paint on an old jalopy,” Mr. Schumer said. “The car still won’t run, the bill still won’t help the American people.”

Conservative lawmakers are being squeezed between groups lining up on different sides of the legislation.

Antiabortion groups, such as the National Right to Life Committee, favor the legislation and have said they would include it on their scorecards of key votes. They support the bill’s one-year ban on Medicaid funding to Planned Parenthood clinics. The U.S. Chamber of Commerce also said it backed the bill and would hold lawmakers accountable for not following suit.

But Heritage Action, the political arm of the conservative Heritage Foundation, says it wants lawmakers to withhold support, because the bill fails to strip many of the ACA’s insurance requirements that they believe have driven up premiums.

Opposing Mr. Trump could prove costly for Republican lawmakers, some political analysts said. In the 2016 elections, then-Sen. Kelly Ayotte lost re-election in New Hampshire after breaking with Mr. Trump following the release of a videotape in which he made crude comments about women.

“What we do know is from the last election there is evidence that Republicans who crossed Trump paid a political price in general elections,” said David Wasserman, the House editor at the Cook Political Report.

The legislation would overturn large parts of the 2010 health law passed by Democrats and replace it with a system largely built on tax credits and cuts to Medicaid.

The proposal would leave 24 million more people uninsured in 2026, compared with maintaining the ACA, according to a report from the Congressional Budget Office that was done before changes were made to the bill Monday. It would also reduce the federal deficit by $337 billion over the next decade.