Senate Armed Services Committee Chairman John McCain speaks during the committee's hearing on foreign cyber threats, on Capitol Hill in Washington, US, January 5, 2017. [Photo/Agencies]

The decision by Senate Majority Leader Mitch McConnell late Saturday came not long after McCain's office disclosed that he had undergone surgery to remove a blood clot from above his left eye. He's expected to be out for the week, recovering in Arizona.

Adding to the uncertainty, the Congressional Budget Office also indicated on Sunday it no longer expected to release its analysis on Monday on the estimated cost and scope of insurance coverage under the latest GOP bill, which has the support of President Donald Trump.

The No 2 Senate GOP leader, John Cornyn of Texas, said he still expected the Senate to move quickly, holding a vote as soon as McCain returns. But amid growing public unease over the bill, some Republicans suggested the delay will make McConnell's task of winning enough support even harder.

In a Senate divided 52-48 between Republicans and Democrats, McConnell can lose no more than two GOP votes and still prevail.

"There are about eight to 10 Republican senators who have serious concerns about this bill. And so at the end of the day, I don't know whether it will pass," said moderate Sen. Susan Collins, R-Maine. She has made clear she would vote against the bill, citing proposed cuts to the Medicaid health program for the poor and elderly.

Sen. Rand Paul, R-Ky., who is also opposed, said doubts also are increasing among Republicans who want to see a fuller repeal of the Affordable Care Act. "The longer the bill's out there, the more conservative Republicans are going to discover that it's not repeal," he said.

The White House said Sunday that Trump was "monitoring what's going on with health care" but did not otherwise weigh in on the growing uncertainty. "We wish Sen. McCain a speedy recovery," said Helen Aguirre Ferre, director of media affairs.

McConnell last week had refashioned the legislation to attract additional GOP votes. The new package added language letting insurers sell discount-priced policies with minimal coverage aimed at winning over conservatives, and revised funding formulas that would mean federal money for states including Louisiana and Alaska — home to four GOP senators who are uncommitted on the measure.

But the health care legislation was already hanging by a thread. McCain's absence meant it would become impossible for the majority leader to round up the votes needed this week to proceed on the bill.