McCain and eight others have expressed doubts about the bill and if they vote "no", it will fail.
Mr McCain's office said the lawmaker, "in good spirits and recovering comfortably at home with his family", would recover in Arizona through next week.
The rare joint letter from the two major insurer groups is also a departure from insurers' general stance throughout the ObamaCare repeal debate, where they have usually declined to take a firm position either in favor or against the GOP bills. Surgeons in Phoenix removed a blood clot from above McCain's left eye on Friday.
McConnell's announcement came shortly after McCain's office issued a statement disclosing the surgery and noting that doctors had advised the senator to stay in Arizona next week to recover.
Senate Majority Leader Mitch McConnell announced Saturday that he will delay consideration of health care legislation in light of Sen.
Until McCain's surgery, McConnell had hoped to vote on the Republican plan in the coming days.
"I don't see a lot here that would meaningfully change the CBO score", said Cynthia Cox of the non-partisan Kaiser Family Foundation, a think-tank focusing on health policy, in an interview on Friday with Business Insider. The absence of McCain would mean that a maximum of 49 votes would be available to vote "yes".
The GOP also inserted a provision into the latest bill that would exempt members of Congress and their staffs from no longer receiving essential health benefits.
The future of the Republicans' health care bill is once again in peril this week after Sen.
The Senate Health Care bill faces an uncertain future.
"But if we are not able to reach a consensus, the Senate should return to regular order, hold hearings, and receive input from senators of both parties, and produce a bill that finally provides Americans with access to affordable and quality health care".
A previous version of the health-care bill was pulled from the floor of the House of Representatives in March after it failed to gain enough votes to advance.
This reduction in spending that is favored by conservatives like Johnson but worries moderates in states with large Medicaid populations like Capito, who represents West Virginia.