Heller, like four other GOP senators who announced their opposition to the Obamacare repeal bill that was unveiled Thursday, left the door open to negotiations. Mike Lee (R-Utah), Ted Cruz (R-Texas), and Ron Johnson (R-Wis.) released a joint statement saying they were "not ready" to support the legislation.
McConnell must navigate a narrow route in which defections by just three of the 52 Republican senators would defeat the legislation.
The 142-page proposal, worked out in secret by Senate Majority Leader Mitch McConnell with other Republican leaders, was welcomed by President Donald Trump.
But Trump has made a slight about-face about health care reform since cheering the House bill during a Rose Garden ceremony.
Polls show that a majority of Americans are in opposition to the House version of this legislation, and with good reason.
The doubts about the latest plan from Washington came from Republicans, Democrats and the nation's one independent governor.
Medicaid expansion in Pennsylvania has allowed more than 15,000 newly eligible Bucks residents to get health coverage, Jonathan Rubin, director of the Bucks County Division of Human Services told this news organization after the House released its version of the bill. Republicans say it costs too much and involves the federal government too much in healthcare. "And policies contained in the discussion draft will repeal the individual mandates so Americans are no longer forced to buy insurance they don't need or can't afford", McConnell said. The Senate bill also calls for a tighter cap on federal spending in Medicaid overall than the House bill did.
It, however, delays cuts to the Medicaid programme and maintains for two years the tax credits included in the Affordable Care Act - commonly known as Obamacare - to help lower-income Americans purchase coverage.
Greg Valliere, the chief strategist and a longtime political analyst at Horizon Investments, said in a note to clients Friday that the conservative members besides Paul were likely to relent since failure to pass the bill "would mean Obamacare wins".
The premise of the bill, repeated nearly daily in some form by its chief author, McConnell, is that "Obamacare is collapsing around us, and the American people are desperately searching for relief".
"Polls support the opponents - and Barack Obama, still popular, will lead the charge", Valliere said. Senate leaders are aiming for a vote before July 4.
"The answer is that it is affecting funding for critical services that we provide", he said.
Here are the key aspects of the Senate bill to keep in mind.
"There isn't anything in this bill that would lower premiums", Heller said. "As we await a score and then consider amendments on the floor, I welcome the feedback of Kansans".
"Republicans believe we have a responsibility to act - and we are".
The Senate bill is also much like the House bill in that it would repeal most of the taxes associated with Obamacare (it would bump out the implementation of the so-called Cadillac tax on expensive, employer-sponsored health care plans, from 2025 to 2026).
"No argument against Trumpcare is more eloquent than the grave consequences it means in people's lives", she wrote colleagues.
AVIK ROY: The bill will encourage a lot more of those individuals to buy health insurance.
The Senate bill would provide money to stabilise the individual insurance market, allotting US$15 billion a year in 2018 and 2019 and US$10 billion a year in 2020 and 2021.
However, under Senate rules, there's a chance abortion restrictions on private insurance plans may be struck down.
The nonpartisan Congressional Budget Office (CBO) has estimated that the House bill would kick 23 million people off their healthcare plans. He could not immediately point to anything in it that would keep him from voting for it, although he said he expected changes to the bill in the Senate.
"The Medicaid cuts are even more draconian that the House bill was, though they take effect more gradually than the House bill did", Pearson says.
A statement from Capitol Police said, "Many of the demonstrators, as part of their protest activities, removed themselves from their wheelchairs and lay themselves on the floor, obstructing passage through the hallway and into nearby offices".
USA hospital stocks were trading sharply higher after the bill was released.