After the Congressional Budget Office (CBO) score, Senator Susan Collins, a moderate Republican, said she could not support moving forward on the bill as written.
Collins' opposition highlights the delicate balance that Senate Majority Leader Mitch McConnell must strike as he tries to deliver a legislative win to President Donald Trump by reconciling the Republican Party's moderate and conservative wings.
Moderate senators are concerned about millions of people losing insurance. Key conservative senators have said the Senate bill does not do enough to repeal Obamacare.
The CBO assessment that an additional 15 million people would be uninsured in 2018 under the bill and its prediction that insurance premiums would skyrocket over the first two years prompted concern from both sides.
McConnell's goal was to have a vote on the bill before the July 4 recess that starts at the end of this week. But several Republicans, including Collins, have said they would not approve a procedural motion that would clear the way for a vote.
McConnell can afford to lose just two Republican senators from their 52-seat majority in the 100-seat Senate, which would allow passage of the bill with Vice President Mike Pence casting the tie-breaking vote.
"If you are on the fence ... this CBO score didn't help you, so I think it's going to be harder to get to 50, not easier," Republican Senator Lindsey Graham said of the bill's prospects.
The CBO score is also likely to amplify criticism from industry groups such as the American Medical Association, which said earlier on Monday that the Senate's bill violated the doctors' precept of "first, do no harm."
The CBO is only able to assess the impact of legislation within a 10-year window, but it said that insurance losses are expected to grow beyond 22 million due to deep cuts to the Medicaid insurance program for the poor and disabled that are not scheduled to go into effect until 2025.
Trump and Republicans in Congress made repealing and replacing Obamacare, former Democratic President Barack Obama's signature domestic legislation, a central campaign promise. The pressure is on for them to deliver now that they control the White House, House of Representatives and Senate.
Republicans view Obamacare as costly government intrusion and say that individual insurance markets are collapsing. Obamacare expanded health coverage to some 20 million Americans by expanding Medicaid and mandating that individuals obtain health insurance.
The CBO score was released just hours after Republicans revised the bill, adding a measure that would penalize people who let their insurance coverage lapse for an extended period. The move followed criticism that the original bill would result in a sicker - and more expensive - insurance pool.
WHITE HOUSE ROLE
At least four conservative Republicans - Senators Ted Cruz, Rand Paul, Ron Johnson and Mike Lee - have expressed opposition to the Senate legislation.
Moderate Republicans have warned against replacing Obamacare with legislation that is too similar to the version passed by the House, saying it would cause too many people, especially those with low incomes, to lose health coverage.
The CBO estimated that the House bill would cause 23 million people to lose insurance. Trump had called the House bill "mean" and asked Senate Republicans to come up with "more generous" legislation.
Democrats uniformly oppose both the House and Senate versions of the bill.
"CBO's report today makes clear that this bill is every bit as 'mean as the House bill," Senator Chuck Schumer, the Democratic leader, told reporters.
The White House in a statement on Monday criticized the CBO for issuing a "flawed report" and said its assessments should not be "trusted blindly."
Trump and McConnell have been working to shore up support.
The president called key conservative senators over the weekend, White House spokesman Sean Spicer said.
Both Cruz and Johnson said they were concerned about CBO estimates that insurance premiums would initially rise as much as 30 percent over the first two years before declining.
"Doesn't help the people whose premiums skyrocket next year," Cruz told reporters.
"Kind of a problem, isn't it?" Johnson said of the short-term premium increase.
Johnson and Paul have said they will oppose the procedural motion that would allow the Senate to move forward to a vote. Cruz is drafting suggested fixes. Paul remains opposed to the bill.
The first moderate Republican to oppose the bill, Senator Dean Heller, is already facing political fallout. America First Policies, a political group run by former Trump campaign staffers, said it would air healthcare-related attack ads against Heller, who faces a competitive re-election race in Nevada next year.
Senator Rob Portman, of Ohio, who has not said whether he supports the bill, was "dressed down" by McConnell during a Monday leadership meeting, a senior Republican aide told Reuters.
Ohio participates in Obamacare's Medicaid expansion, and Republican Governor John Kasich has criticized the Senate bill. Portman's office did not respond to a request to comment.
Senator Marco Rubio of Florida said his governor, fellow Republican Rick Scott, would be on Capitol Hill this week to discuss the bill's impact on the state.
Constituent and industry groups have been critical of the Senate bill's proposal to reduce the Medicaid healthcare program for the poor and point to the CBO analysis that it would disproportionately affect older adults.
Under Senate rules, the bill must replicate savings projected in the House version that passed last month. It cleared that critical hurdle, with the CBO estimating it would decrease the budget deficit by $321 billion over 2017-2026.
A revision to the bill that imposes a penalty for prolonged lapses in insurance coverage addresses the original bill's provision to drop the Obamacare penalty on those who do not have insurance. Experts had warned that canceling the fine could lead to a sicker insurance pool because young and healthy people would not face consequences for failing to purchase insurance.
The bill would impose a six-month waiting period for anyone who lets their health insurance lapse for over 63 days and then wants to re-enroll in a plan in the individual market.
The 15 million people the CBO estimates would be uninsured in 2018 is largely due to the repeal of the penalty associated with being uninsured. The CBO did not evaluate the revised version that included the new waiting period.
Insurer Blue Cross and Blue Shield said it was encouraged by the inclusion of incentives for continuous coverage. Molina Healthcare said it preferred the Obamacare mandate, said that and the Senate bill, even after revised, would simply delay care.
If the Senate passes a bill, it will either have to be approved by the House, the two chambers would have to reconcile their differences in a conference committee, or the House could pass a new version and bounce it back to the Senate.