On Friday, Mr. Pence assured skeptical governors that “the Senate health care bill strengthens and secures Medicaid for the neediest in our society,” putting the program, which serves more than 70 million low-income people, on “a path to long-term sustainability.”

But Ms. Collins said: “I would respectfully disagree with the vice president’s analysis. This bill would impose fundamental, sweeping changes in the Medicaid program, and those include very deep cuts. That would affect some of the most vulnerable people in our society, including disabled children, poor seniors. It would affect our rural hospitals and our nursing homes. And they would have a very difficult time even staying in existence.”

She added, “There are about eight to 10 Republican senators who have serious concerns about this bill.”

Republicans hold 52 Senate seats, and all Democratic senators oppose the bill. Ms. Collins and Senator Rand Paul, Republican of Kentucky, have said they will vote against even starting the debate, meaning all other Republican senators need to vote for the legislation if it is to pass.

Mr. Paul’s reasons for opposing the bill are very different from Ms. Collins’s; he says it retains too much of the Affordable Care Act. And he predicted that support for the legislation would erode because of the delay prompted by Mr. McCain’s absence.

“The longer the bill’s out there, the more conservative Republicans are going to discover that it’s not repeal,” he said Sunday on CBS’s “Face the Nation.” “And the more that everybody’s going to discover that it keeps the fundamental flaw of Obamacare. It keeps the insurance mandates that cause the prices to rise, which chase young, healthy people out of the marketplace and leads to what people call adverse selection, where you have a sicker and sicker insurance pool and the premiums keep rising through the roof.”

Voters “elected us to repeal Obamacare,” Mr. Paul added. But with the bill drafted by Mr. McConnell, the senior senator from his home state, he said, “we’re going to keep most of the taxes, keep the regs, keep the subsidies and create a giant bailout superfund for the insurance companies.”