The United States Conference of Catholic Bishops said the Senate bill was “unacceptable as written” and would “wreak havoc on low-income families.” At the same time, the bishops said they liked two sections that seek to “prohibit the use of taxpayer funds to pay for abortion or plans that cover it.”

Republicans are finding allies to be few and inconstant. Mr. Trump has said he is “very supportive” of the Senate bill. But that support will be of limited help to Mr. McConnell. Few senators feel loyal to Mr. Trump, whose erratic message has often weakened his influence on Capitol Hill.

After pushing for passage of the House repeal bill, he criticized it as “mean” several weeks later. A spokeswoman, Sarah Huckabee Sanders, said last week that Mr. Trump did not necessarily support cuts to Medicaid, even though his budget and the Senate bill would make such cuts.

Kellyanne Conway, a top adviser to Mr. Trump, claimed on Sunday that the Senate bill did not actually cut Medicaid. Ms. Collins said, “I respectfully disagree with her analysis.”

So far, five Republican senators have announced that they cannot support the bill as drafted: Dean Heller of Nevada, who says it cuts coverage too deeply, and four conservatives — Rand Paul of Kentucky, Ted Cruz of Texas, Mike Lee of Utah and Mr. Johnson — who say it does not do enough to lower health costs. Other Republicans, like Ms. Collins and Senator Lisa Murkowski of Alaska, have expressed misgivings, and Senator Ben Sasse of Nebraska declined to say Sunday how he would vote.

Senate leaders, trying to muster support, are looking for ways to address a conspicuous omission: The bill requires insurers to accept anyone who applies, but repeals the mandate for people to have coverage and does not replace it with anything. So people could wait and buy insurance only when they need it. Insurers say they need large numbers of healthy people to help pay for those who are sick.