A top Senate Republican has vowed to bring the party's healthcare bill to a vote as soon as possible, even as detractors said they would use a delay caused by the absence of Senator John McCain to mobilise further opposition to the measure.

"I believe as soon as we have a full contingent of senators, that we'll have that vote," the No. 2 Senate Republican, John Cornyn of Texas, said on NBC's Meet the Press.

But questions emerged over when that might be. McCain, 80, had a craniotomy - a procedure in which doctors create an opening in the skull - on Friday to remove a blood clot above his left eye, and he is recovering at home in Arizona. A statement from his office had indicated that he would be out this week, but neurosurgeons not involved with McCain's surgery said the recovery period for such a procedure was often longer.

"For most patients, the time to recover from a craniotomy is usually a few weeks," said Dr Nrupen Baxi, an assistant professor of neurosurgery at the Albert Einstein College of Medicine in New York City.

McCain's surgeons are not giving interviews, and his communications director, Julie Tarallo, said no further information was available.

Aides to the Senate majority leader, Mitch McConnell of Kentucky, said it was unclear how long the delay would last.

The timing of the Senate vote is crucial. The more it is delayed, the more likely the bill is to fail, supporters and opponents say. Moreover, the Senate schedule will soon be packed with other legislation, like an increase in the statutory limit on federal borrowing and spending bills for the fiscal year that starts on October 1. In addition, Republicans are eager to cut taxes and simplify the tax code.

The Senate has struggled to pass a healthcare bill, delaying a vote on a previous version of the legislation in June. Several Republican senators have expressed reservations or outright opposition to the new version as well, and Republicans need McCain's vote to have any chance of passing it.

The bill, to repeal and replace major provisions of the Affordable Care Act, is a priority for President Donald Trump and Republicans in the House, which passed its own repeal bill in early May.

Cornyn acknowledged that "there's uncertainty about what the final outcome will be". Asked what would happen if the bill did not pass, he said: "I assume we'll keep trying. But at some point, if Democrats won't participate in the process, then we're going to have to come up with a different plan."

Critics of the Senate's healthcare bill, taking advantage of the delay, said at the weekend that Republican leaders needed to rework the legislation in fundamental ways. Given the additional time, they said, Senate committees should hold hearings to solicit opinions from the public and from experts on healthcare and insurance.

"We should not be making fundamental changes in a vital safety net program that's been on the books for 50 years, the Medicaid program, without having a single hearing to evaluate what the consequences are going to be," Senator Susan Collins, a Republican from Maine, said on CNN's State of the Union.

Roughly 20 million people have gained coverage through the Affordable Care Act, a pillar of President Barack Obama's legacy. But Cornyn described the law as a failed "exercise in central planning and command and control".