Patty Murray, who lead the Senate Health, Education, Labor and Pensions Committee, has been put on hold since the Graham-Cassidy bill emerged.
The Graham-Cassidy bill would redirect health care funds to the states and give them more control over how to use the money, but critics say the legislation would result in significant funding cuts and leave millions uninsured.
Trump alleged that McCain had been influenced in his decision by Senate Minority Leader Chuck Schumer (D-N.Y.) in his decision to oppose the bill co-authored by Sens.
President Trump has been phoning lawmakers and state governors in a bid to tilt the scales in favour of the bill but several Republican governors this week also criticised the process as rushed.
"The only way you know how people will vote is you have the vote", he said.
The GOP's predicament was summed up bluntly by Sen. Lamar Alexander and Democratic Sen.
The focus now shifts to two female GOP moderates, Sens. Lisa Murkowski (R-AK) and Susan Collins (R-ME) voted against the "skinny" Obamacare repeal bill.
If Collins comes out against the bill, crafted by GOP Sens. She has, however, criticized Graham-Cassidy and echoed McCain's calls for bipartisan efforts to address health care concerns.
Speaking in Alabama, he said senators from his party who opposed the repeal lacked "the guts to vote for it".
Likewise, Murkowski voted against the previous GOP health care bills and has not yet declared her position.
If one of the two senators announces opposition to the latest bill, it can not pass the Senate.
Under current Senate budget rules, the Republicans have until September 30 to pass legislation with a 50-vote margin instead of 60 votes, meaning just three Republican senators could scuttle the bill.
The bill, authored by Sens. Lindsey Graham of SC would have unraveled the central elements of Obama's law, including the requirement for Americans to carry health insurance or pay fines, and offered block grants to states to design their own systems with less federal control. John McCain, has begun physically mocking them in private, Axios reported on Wednesday. "I would consider supporting legislation similar to that offered by my friends Senators Graham and Cassidy were it the product of extensive hearings, debate and amendment".
The president imitates McConnell by slumping his shoulders and looking lethargic, and emulates the dramatic thumbs down McCain used to indicate his "no" vote on the GOP healthcare bill in July.
Paul said he opposes the bill because it doesn't go far enough in repealing the Affordable Care Act, by maintaining numerous taxes while redirecting the funds to states. "I won't vote for Obamacare Lite that keeps 90% of the taxes & spending just so some people can claim credit for something that didn't happen", Paul tweeted on Friday.
Trump has pressured his fellow Republicans for quick passage on what would be his first victory on major legislation.