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WASHINGTON — The Senate expects to hold a vote on the revised Republican health care bill once Sen. John McCain recovers from surgery for a blood clot above his left eye, Senate Majority Whip John Cornyn said Sunday.

The Arizona senator's unexpected announcement Saturday that he needs time to recover from the minimally invasive procedure led Senate Majority Leader Mitch McConnell to say he was postponing a planned vote related to the bill this week.

McCain's sudden absence also shows the fragility of the GOP coalition on health care legislation — one that is supposed to be a hallmark of President Donald Trump's administration to dismantle the Affordable Care Act, or "Obamacare."

"We wish John McCain a speedy recovery, and we need him in more ways than one," Cornyn, R-Texas, said in an exclusive interview on "Meet The Press."

Related: McConnell Delays Health Care Vote As McCain Recovers From Surgery

"But yes, I believe that when we have a full contingent of Senators that we’ll have that vote and it’s important that we do so," he added.

Get well soon, John. We need you in more ways than one! https://t.co/hgFfxYQhea — JohnCornyn (@JohnCornyn) July 16, 2017

It's unclear how long McCain might be sidelined and the vote delayed.

The Mayo Clinic Hospital in Phoenix released a statement Saturday that said McCain's surgery Friday was successful: "The Senator is resting comfortably at home and is in good condition. His Mayo Clinic doctors report that the surgery went very well and he is in good spirits."

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The loss of McCain has cast the success of the Senate's health care bill in question since McConnell needs 50 votes to advance the bill. There are only 52 Republicans in the Senate, and two of them — Sens. Rand Paul, R-Ky., and Susan Collins, R-Maine — have already announced they won't support moving the bill forward to even begin debate on it.

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"While John is recovering, the Senate will continue our work on legislative items and nominations, and will defer consideration of the Better Care Act," McConnell said Saturday.

A nonpartisan Congressional Budget Office score on the legislation was expected early this week. A spokesperson for the Senate Budget Committee said Sunday that the CBO will not release a score on Monday. The date that the score will be released is not clear.

The Republican proposal received more tough news this weekend with a new ABC News/Washington Post poll that found more people prefer to keep the Affordable Care Act to the proposed Republican health care bill by a two-to-one margin.

Cornyn on Sunday ascribed those poor numbers to criticism of the legislation.

"That's mainly because all they hear is the critics, but the fact is we know millions of people are seeing sky-high premiums, unaffordable deductibles and fleeing insurance markets because insurance companies keep losing money," he said.

Senate Republicans released a revised version of their health care bill on Thursday in an attempt to appease some of the lawmakers who were previously unconvinced.

The changes included a version of an amendment from Sen. Ted Cruz, R-Texas, that allows insurers to sell cheaper but less comprehensive plans in the individual health care market if they also offer a plan compliant with Obamacare standards. Revisions also include $45 billion more aimed at fighting opioid addiction, an extension of taxes on the wealthy under the Affordable Care Act and more provisions aimed at satisfying some specific senators who have been on the fence.

"I think this bill has actually gotten much better as a result of the discussions we've had amongst ourselves," Cornyn said. "I think it's something that once we agree, that we can sell to the American people as a better choice than the failures of Obamacare."

The delay in voting this week could have an effect on how people perceive the bill, Paul said Sunday on CBS's "Face the Nation."

Related: Governors 'High Degree of Anxiety' Over Health Care Bill

"You know, I think the longer the bill's out there, the more conservative Republicans are going to discover that it's not repeal — and the more that everybody's going to discover that it keeps the fundamental flaw of Obamacare," he said.

Collins, meanwhile, told CNN that she has serious doubts about whether or not this version of the legislation will ever make it through the Senate.

"There are about eight to 10 Republican senators who have serious concerns about this bill," she said. "And so, at the end of the day, I don't know whether it will pass."

Democrats also have their doubts about the bill's future.

Senate Minority Leader Chuck Schumer said Sunday that he did not think delaying the vote on it during McCain's recovery "changes the outcome."

"Time is not the problem in the present healthcare bill. The problem is the substance," the New York senator told reporters. "It slashes Medicaid, which has become something that helps middle-class New Yorkers, millions of them literally, and millions of Americans."

"So my plea is very simple to Leader McConnell: This bill should be scrapped because it hurts middle-class Americans too much, at the same time that it gives tax breaks to the wealthiest among us," Schumer said, adding that the solution was for Democrats and Republicans to "sit down and work together on improving Obamacare."