Two Republican senators, Susan Collins of Maine and Rand Paul of Kentucky, have said they oppose the bill in its current form, for very different reasons, and will not vote even to begin debate.
Mr. McCain, 80, announced Saturday night that he had the surgery at Mayo Clinic Hospital in Phoenix. He is at home with his family and, âon the advice of his doctors,â will be recovering in Arizona this week, a spokeswoman said.
Any delay in the Senate will give critics more time to mobilize opposition to the bill. The opponents include consumer groups, patient advocates and organizations representing doctors, hospitals, drug abuse treatment centers, insurance companies and religious leaders.
Mr. McCain has been decidedly noncommittal in his comments on the bill. Its passage is a top priority for President Trump and Republicans in Congress.
Hundreds of thousands of people in Arizona have gained coverage through the expansion of Medicaid under the Affordable Care Act, and Mr. McCain was planning to propose amendments to the bill to protect his constituents.
Asked last month about the chances for a quick agreement among Republican senators on a bill, Mr. McCain said that âpigs could fly.â
A number of other Republicans have expressed serious reservations about the bill in its current form. They include Senators Shelley Moore Capito of West Virginia, Dean Heller of Nevada, Lisa Murkowski of Alaska and Rob Portman of Ohio.
The House passed a repeal bill, broadly similar to the Senate measure, by a vote of 217 to 213 in early May. Mr. McConnell was forced to put off a vote when it became evident he did not have the votes he needed in the Senate.
Governors of both parties have sharply criticized the Senate bill, drafted mainly by Mr. McConnell. Trump administration officials are frantically trying to win over state officials gathered in Providence, R.I., this weekend for a meeting of the National Governors Association.
The administration is trying to discredit estimates by the Congressional Budget Office that more than 20 million people would lose insurance coverage by 2026 as a result of the Senate and House bills.