House Republicans on Thursday are set to vote on a bill that calls for the repeal and replacement of one of President Trump's favorite targets: ObamaCare.

"We're gonna pass it," House Majority Leader Kevin McCarthy, R-Calif., told Fox News Wednesday night. He said the new bill had the support to head to the Senate.

An amendment proposal by Reps. Fred Upton, R-Mich., and Billy Long, R-Mo., adds $8 billion to the measure over a five-year span to help some people with pre-existing medical conditions afford coverage.

The overall bill would cut Medicaid, repeal tax boosts on higher-earning people, eliminate ObamaCare's fines on people who don't buy insurance and give many of them smaller federal subsidies. The bill, if passed, would move on to the Senate, where it would likely face more difficulty.

Upton, who had been opposed, was seen as a significant supporter because he's a respected, centrist voice on health issues and former chairman of the House Energy and Commerce Committee.

Upton and Long were among four House members who met with Trump at the White House on Wednesday.

"Today we're here announcing that with this addition that we brought to the president, and sold him on in over an hour meeting in here with him, that we're both yesses on the bill," Long told reporters at the White House."'We need you, we need you, we need you,"' Long described as the message from Trump.

The New York Times wrote that if the bill passes, “it would be a moment of redemption for both Mr. Ryan and Mr. Trump, who suffered a resounding political defeat in March when they failed to muster the votes to win approval of an earlier version.”

Sen. Chuck Schumer, D-N.Y., criticized the proposal, saying the Upton amendment is like “like administering cough medicine to someone with stage-four cancer,” he said in a statement. “This Republican amendment leaves Americans with pre-existing conditions as vulnerable as they were before under this bill.”

The bill's passage would mark the culmination of seven years' worth of promises by Republicans to undo Obama's signature legislative achievement and provide a long-sought win for President Trump, who has been in office more than 100 days without a significant congressional victory save the Senate confirmation of a Supreme Court justice.

The latest iteration of the GOP bill would let states escape a current requirement that insurers charge healthy and seriously ill customers the same rates, a measure that has drawn the ire of some moderate Republicans.

The American Medical Association, AARP and other consumer and medical groups are also opposed. The AMA issued a statement saying Upton's changes "tinker at the edges without remedying the fundamental failing of the bill - that millions of Americans will lose their health insurance as a direct result."

Before the White House meeting, House Speaker Paul Ryan, R-Wis., praised the proposal and said the GOP was getting "extremely close" to finally being able to pass the stalled legislation.

The existing health care measure would let states get federal waivers allowing insurers to charge higher premiums to people with pre-existing illnesses who'd let their coverage lapse. To get the waiver, the state must have a high-risk pool or another mechanism to help such people afford a policy.

Opponents said that would effectively deny such people coverage by letting insurers charge them unaffordable prices. They say high-risk pools have a mixed record because government money financing them often proves inadequate.

There's already around $130 billion in the legislation states could use to help people afford insurance, but critics have said that's just a fraction of what would be needed for adequate coverage.

Fox News' Chad Pergram contributed to this report