Republican Representative Mark Meadows, chairman of the conservative House Freedom Caucus, said the roughly three dozen members have decided not to vote as a bloc.
Wednesday also brings the last official procedural stepping stone before the bill heads to the House floor - the Rules Committee, a panel traditionally full of leadership loyalists, which should clear the way to consider amendments to the measure and set up Thursday's dramatic vote.
Asked by reporters if he'd keep pushing a health overhaul if the House rejects the measure, Trump said, "We'll see what happens".
"These are the conservative solutions we campaigned on and these are the conservative solutions the American people asked us to deliver", Trump said at a National Republican Congressional Committee fundraiser Tuesday night.
"There is no Plan B. There is Plan A and Plan A. We're going to get this done", White House spokesman Sean Spicer said.
Over the next 48 hours, Trump is expected to keep working the phones and meeting face-to-face with lawmakers at the White House.
He says, "Thursday is the big day".
The House can not have more than 21 defections if all Democrats decline to approve the plan. Republicans said the plan sets aside $85 billion over 10 years for that goal. "You can't go promise over and over again" and not deliver, Spicer said.
Senate Minority Leader Chuck Schumer, D-N.Y., and other Democrats will try removing provisions from the GOP bill cherished by conservatives: letting states require some Medicaid recipients to work and barring federal health subsidies from use for abortions.
"Oh, he was kidding around", said Representative Harold Rogers (R-KY), a supporter of the bill, about Trump's threats.
He declined to say what he would do if the proposed legislation fails in the House.
During the meeting with lawmakers on March 21, Trump said the time to repeal Obamacare, also known as the Affordable Care Act, is now, and that failure to do so could have serious repercussions.
Republicans can only afford to lose two of their own party members in the Senate, in which they hold a 52-seat majority.
"Despite the proposed amendments, I still can not support the House health-care bill, nor would it pass the Senate".
The ads, airing only through Wednesday, call the House bill "Ryancare", after House Speaker Paul Ryan of Wisconsin, and "a bad idea doubling down on disaster".
The ad script reads: "Don't fall for fake repeal".
Ryan said, "President Trump was here to do what he does best and that is to close the deal". If it passes, the bill faces an uncertain future in the Senate.
Some conservative lawmakers believe the healthcare bill does not go far enough, while moderate Republicans worry that millions of Americans will be hurt by the dismantling of the 2010 Affordable Care Act, Democratic former President Barack Obama's signature healthcare legislation. "Honestly, a loss is not acceptable, folks".
FBI Director James Comey said the bureau is investigating whether Trump campaign associates coordinated with Russian officials as Moscow sought to sway the US presidential election. "If you don't pass the bill there could be political costs". The White House seemed to make progress with the hardliners while House leaders struggled with moderates ahead of a showdown vote.
Nancy Nielsen, associate dean for health policy at the University at Buffalo's Jacobs School of Medicine, said Republican leaders were in a tough spot.
Mark Meadows, who heads the conservative House Freedom Caucus, said after a White House meeting with Vice President Mike Pence that his group had more than enough members to stop the bill from passing, although he remained hopeful for potential changes to the legislation.
The president said to Republicans, we're going to be so embarrassed Thursday if we vote this down. Rebellion among House Republicans also would undercut Trump's image as a dealmaker, jeopardizing his ability to muscle through tax reform, infrastructure projects, immigration and other issues. The House vote is scheduled in just two days. There was no such provision in Monday's changes.
To address criticism that the bill would leave many older people with higher costs, GOP leaders have taken an unusual approach.
The bill would let the Senate approve tax credits more generous to people age 50 to 64.