Democrats said they will use procedural tactics to slow the Senate's work in an effort to focus attention on the Republican effort.
Since Obamacare became law in 2010, Republicans have campaigned on repealing the program that extended insurance coverage to millions of additional Americans through both subsidized private insurance and an expansion of Medicaid.
GOP Senate leaders were eager to get a seal of approval from Trump, who had urged them to produce a bill more "generous" than the House's.
Unlike the House plan that passed before lawmakers got an updated cost, the Senate has to get those numbers from the Congressional Budget Office before they vote. Senate Majority Leader Mitch McConnell has faced backlash for the perceived lack of transparency behind the health care bill negotiations, but insisted that there will be "plenty of time" for discussion. But Republicans from states that expanded Medicaid, like Ohio's Rob Portman, want to extend that to seven years.
The bill will ultimately be judged by what is in it, and not the way it was drafted. Shelley Moore Capito has said she has concerns with the House version of the bill, but has not said whether she will support the Senate's revised plan. "That's an issue", she said.
But the Senate GOP bill could face a tougher road.
Even some of the 13 members who are supposed to be writing it say they haven't seen any details.
Scalise upgraded from 'critical' to 'serious' condition
Aguilar plays outfield for the Democratic team; before the shooting , Scalise was slated to play second base for the Republicans . House Majority Whip Steve Scalise looks like he will make an "excellent recovery", doctors say - but that wasn't always the case.
Aides and lobbyists said they expected the GOP bill to provide health care tax credits linked to people's incomes, not their ages like the House-passed measure, and impose spending limits on the growth of the federal-state Medicaid program for the poor that would tighten further by the mid-2020s.
With a 52-48 majority in the Senate, Republicans can only afford to lose two votes in order to pass the bill, which would repeal and replace Obamacare. The bill will be brought to the Senate floor once the CBO has assessed its cost and impact, "likely next week", McConnell said.
Paul said he won't know how he will vote until the bill is released to legislators on Thursday, but he anticipates that McConnell won't have the votes and will have to renegotiate the legislation with members of his own party.
Vice President Mike Pence predicted that new healthcare legislation would be enacted this summer.
Brady said that he believes the problem can be fixed by the Senate, which may have to find a way to vote on a different version of the bill, even as Senate leadership tries to clear the decks of major items like health care reform and raising the debt ceiling.
The columnist warned President Donald Trump's administration and Republicans in Congress in February about the potential repercussions of failing to repeal and replace Obamacare.