Republican lawmakers are trying to rally votes to pass a new health bill this week after their previous attempt two months ago collapsed in disarray.
Mr Trump insists the new measure covers Americans with pre-existing conditions "beautifully".
But even many Republicans say the bill undermines that popular element of President Barack Obama's signature law.
Republicans withdrew a healthcare bill in March to replace the Affordable Care Act (ACA), also known as Obamacare, after they were unable to secure enough support to pass it.
The withdrawal embarrassed the president, who has repeatedly vowed to repeal and replace his predecessor's accomplishment.
It was also viewed as a major setback for Republicans, who were unable to rally behind the party's long-held goal to repeal the law, despite control of both the House and Senate.
Moderate Republicans were unhappy that the bill cut health coverage too severely, while more conservative lawmakers felt the changes did not go far enough.
It has an amendment designed to woo hard-line conservatives, allowing states to ditch key Obamacare insurance regulations.
It keeps an Obamacare clause requiring insurers to provide coverage to those with pre-existing conditions, however, it also allows insurers to charge higher rates to those same patients.
States could obtain a waiver to allow insurers to charge higher rates based on the "health status" of a person if they let their coverage lapse.
Insurers could also offer policies that limit benefits for those with pre-existing conditions, which could affect the quality of policies.
The new bill's amendment also allows states to apply for permission to opt out of the law's essential health benefits, including maternity, emergency care and mental health.
At the centre of debate is whether the new amendment protects Americans with pre-existing conditions such as cancer or diabetes.
House of Representatives Speaker Paul Ryan insisted on Tuesday that "there are a few layers of protections for pre-existing conditions".
Mr Trump told Bloomberg News on Monday: "I want it to be good for sick people. It will be every bit as good on pre-existing conditions as Obamacare."
But critics say the new bill will allow insurance companies to charge sick people at significantly higher rates, ultimately pricing them out of the market.
The American Medical Association, the Association of Medical Colleges and other consumer advocacy groups have called on Congress to vote against the measure.
How disastrous for Trump is healthcare collapse?
The rise of Obamacare: Why is the ACA so popular?
With Democrats united in opposition, House Republicans are currently short of the 216 votes they need to pass the bill before the Senate could take it up.
They can afford only 22 defections, and the latest whip counts put Republican "no" votes at about 20, with a dozen more undecided.
Though the amended bill has brought some hard-line conservatives on board, moderate Republicans are hesitant to support a measure that is perceived to weaken protections for sick Americans.
Top Republican Fred Upton came out against the measure on Tuesday, saying he was "not at all comfortable" with removing protection for people with pre-existing conditions.
House Republican Billy Long, who campaigned against Obamacare in 2010, says he will not support the bill.
The Missouri lawmaker said it "strips away any guarantee that pre-existing conditions would be covered and affordable".
No vote has been formally scheduled.

Sum: President Donald Trump's latest attempt to repeal and replace Obamacare is hanging in the balance.
Q: Around 2,900 athletes will come to Glasgow to take part in cycling, rowing, swimming and triathlon events, while Berlin will stage athletics.
Organisers also hope to include golf at the 2014 Ryder Cup venue Gleneagles.
Scottish minister for sport Jamie Hepburn said it "will be another chance for Scotland to prove it's the perfect stage for top class events".
The new event is different from the European Games, another multi-sport competition being held for the first time this summer in Baku, Azerbaijan.
It is expected to attract a television audience of 850 million thanks to a deal with the European Broadcasting Union, which has 72 members in 56 countries.
Funded jointly by the Scottish government and Glasgow City Council, the European Sports Championships will use many of the 2014 Commonwealth Games venues.
Swimming will be at Tollcross in Glasgow, while diving and synchronised swimming will be at the Royal Commonwealth Pool in Edinburgh. The open water swimming competition will be at Loch Lomond.
The four cycling championships - track, road race, mountain-biking and BMX - will be staged together for the first time, with a new BMX track being built in Glasgow to supplement the Sir Chris Hoy Velodrome and the Cathkin Braes Mountain Bike Trails.
Around 760 athletes will compete in rowing and triathlon events at the Strathclyde Country Park in North Lanarkshire.
And a further 1,500 athletes will compete in Berlin, with the Olympic Stadium hosting the athletics.
Hepburn added: "Last summer, Scotland showed the world what a tremendous job it can do when it comes to staging major sporting events, with the Commonwealth Games and the Ryder Cup both hugely successful.
"As part of the legacy of those events, we want to attract even more top-class sport to Scotland, and the European Sports Championships is certainly in that category."
Scottish athletes will compete under the Great Britain banner during the event.
Councillor Gordon Matheson, leader of Glasgow City Council, said: "We have been chosen because of our excellence and innovation and our proven ability to stage world-class events - not to mention of course our citizens' world-famous warm welcome, so superbly demonstrated during the Commonwealth Games."
Meanwhile, this summer's Baku event will also feature the European Judo Championships, which had been due to take place in Glasgow before a sponsorship row saw the city stripped of the event.

A: Scotland and Germany are to co-host the first European Sports Championships in 2018.
Article: The 22-year-old came through the Championship club's academy but made only 19 appearances for Wolves.
He spent this season out on loan at Shrewsbury and Crawley, scoring twice in 17 matches in all competitions.
"It was close in January - I was nearly coming here on loan and things didn't quite work out," he said.
"As soon as it came about that I was going to be available on a free in the summer, we got back in touch and we've got it done as soon as we could."
McAlinden is Exeter's third summer signing, after Lloyd James and Robbie Simpson.
Find all the latest football transfers on our dedicated page.
++++++++++
Summarize:
Exeter City have signed striker Liam McAlinden on a two-year contract after he was released by Wolverhampton Wanderers earlier this month.