US Senate Republicans have delayed a vote on their healthcare bill until after next week's 4 July Independence Day holiday.
Eight Republican senators have vowed to oppose the bill and the party can only afford to lose two votes to get it passed in the upper chamber.
The announcement by Senate Majority Leader Mitch McConnell is a setback to their plan to replace Obamacare.
US President Donald Trump invited Senate Republicans to the White House for a meeting on Tuesday afternoon.
"This will be great if we get it done," he said.
"And if we don't get it done, it's just going to be something that we're not going to like. And that's okay, and I understand that very well."
The 142-page Senate bill - the Better Care Reconciliation Act of 2017 - phases out the expansion of Medicaid, a government health programme for the low-income Americans, and imposes deep cuts to the programme.
The bill also gives states more latitude in requiring insurers to provide essential health benefits guaranteed under Obamacare, including emergency and maternity care and mental health services.
At least five Senate Republicans had announced opposition to the bill, before the delay was announced. Another three senators joined the rebels hours later on Tuesday.
Moderate Republicans who have opposed the bill criticised it for stripping protections for the poor and elderly, as well as access to women's health.
Conservatives are upset that the bill "does not go far enough" to repeal the Affordable Care Act passed under Barack Obama.
Meanwhile, not a single Democrat is expected to support the proposed legislation having lambasted it as a huge transfer of wealth from poor to rich.
Top Democrat Nancy Pelosi warned that "hundreds of thousands" of Americans would die if the bill passed.
After the delay was announced, Democrats Senate minority leader Chuck Schumer said Republicans "cannot excise the rotten core" of the bill.
The American Association of Retired Persons, the nation's oldest non-profit organisation representing Americans over 50 years old, slammed the bill as an "age tax".
A similar version of the bill has already passed the House, after facing a similar delay.
After Congress returns from the bank holiday, there will be a two-week window before the summer break.
Mr McConnell vowed to continue to try to find the votes, and would make changes to the bill if necessary.
Moderate senators said the bill would harm some of their vulnerable constituents, while conservatives said it had too much government interference.
The news of a delay came just one day after the non-partisan Congressional Budgetary Office said the bill would strip 22 million Americans of health insurance over the next 10 years.