However, more Americans would lose health insurance in the short run under the Senate bill as it stands: an estimated 15 million fewer Americans would have coverage in 2018, compared to 14 million under the House bill.
A conservative Republican senator who doesn't back the GOP health care bill is using unusually sharp tones to criticize party leaders.
Like the House version, the Senate proposal would phase out Obamacare's expansion of Medicaid and change the program's funding from an open-ended entitlement to a fixed budget.
Senate Majority leader Mitch McConnell is trying to reconcile the demands of moderate Republicans concerned about people losing their insurance with those of conservative senators who say the bill does not do enough to repeal Obamacare. The CBO said while most insurance markets would remain stable under the Senate bill, the legislation would drive out insurers that serve a "small fraction" of the population, or these areas will see premiums rise very high.
In a Facebook post last week, former president Barack Obama wrote that the Senate bill would lead to "a massive transfer of wealth from middle-class and poor families to the richest people in America". Spokesperson Sean Spicer said on Monday that Trump had talked over the weekend to Cruz, Paul and Johnson, as well as some others. Employer-based coverage is considered the backbone of the current system, and it's a frequent subject for Republican rhetoric that dictates if people want insurance, they should get a job.
One of the nation's biggest health insurers says the Senate health care bill will "markedly improve" the individual insurance market's stability and moderate premium hikes.
Here is a breakdown of how the Senate legislation stacks up to the House version - the American Health Care Act - and how both compare to Obamacare.
Since it was unveiled last week, the bill has been facing growing opposition from Republicans, with five already declaring that they can not support the current version. That's largely because the penalty for not having health insurance - the Affordable Care Act's so-called individual mandate - would be eliminated.
Also, senators would eliminate the mandates that require almost all Americans to have coverage and companies with more than 50 workers to provide health benefits. At higher income levels, though, younger people would pay a bit less under the Senate bill than under Obamacare - but older Americans could pay much more.
That sort of gambit would rely on the rest of the GOP conference swallowing provisions they don't like, but it's not impossible to envision Republicans going along with a bill that does things they disagree with.
Republicans can only afford to lose two members to pass the bill, which would then come down to a tie-breaking vote by Vice President Mike Pence. The House bill would allow states to opt out of the latter provision. Ron Johnson, who told reporters "I just refuse to be jammed" by leadership on voting for the legislation.