Four Republican opponents could jeopardize McConnell's efforts to pass the measure, which is being moved under rules that allow passage with a simple majority or 50 votes. He supports the expansion of health savings accounts and giving Americans more freedom in choosing plans that are right for them. None of the Senate's 48 Democrats are expected to support the package, meaning the legislation survives only if no more than two Republicans vote no. Sandoval introduced Heller at the press conference with remarks explaining how the Senate bill would lose Nevada hundreds of millions of dollars to cover its low-income population.
That could add Mr Heller's name to Mr Trump's call list.
Healthcare stocks closed down 0.1 per cent on Friday, clawing back some losses after the sector dropped sharply late in the session on Mr Heller's announcement.
It also would end tax penalties on people who don't buy insurance policies and on larger firms that don't offer coverage to workers, while phasing out the extra money given to states that expanded their Medicaid programs to offer insurance to the working poor.
Insurance rates have increased, and we have yet to see the 2018 numbers, but under the Senate bill, cost sharing payments will be covered for few years.
On Fox News Friday, Trump said "It's not that they're opposed".
"It's not that they're opposed", he said.
Mr Trump said getting approval would require traveling a "very, very narrow path" but that "I think we're going to get there".
The bill would also let states apply waivers to disregard some mandates of the Affordable Care Act, like the law's ban on insurance companies charging higher premiums for people with pre-existing medical conditions. Under the Senate GOP plan, all this coverage is at risk. The Senate then took the House bill and, in a rushed, closed-door process, made it harsher. Once promised as a top-to-bottom revamp of the health bill passed by the House last month, the Senate bill instead maintains its structure, with modest adjustments.
Menendez said that the wealthiest Americans will get a tax cut under the Senate legislation, paid for by "taking health care away from those who need it most".