Conservative governors were not much more supportive. Gov. Scott Walker of Wisconsin suggested that Congress consider a better-funded version of the measure proposed this year by two Republican senators, Susan Collins of Maine and Bill Cassidy of Louisiana, that would offer states more flexibility over how to run their health care programs.
Pursuing that approach, Mr. Walker said, would obviate differences between the states that did and did not expand Medicaid while averting the intractable split between conservative and centrist members of Congress over how to structure a replacement. “None of these plans right now do us justice,” he said.
The response mirrored the struggles of congressional Republicans to forge consensus on legislation that would make good on a seven-year vow to repeal the health law. With two Senate Republicans already opposed, Senate leaders cannot lose any additional votes, and on Friday, some of the most influential Republican governors indicated a willingness to torpedo the bill entirely.
Mr. Sandoval’s views are likely to influence Nevada’s Republican senator, Dean Heller, while Mr. Walker’s could play on Wisconsin’s undecided Republican, Ron Johnson.
Recognizing how crucial Mr. Sandoval is, an array of senior federal officials planned to meet with him in Providence for 11th-hour lobbying. The National Governors Association conference, which more typically includes as much recreation as work, attracted Vice President Mike Pence, Health and Human Services Secretary Tom Price and Seema Verma, the administrator of the Medicaid program.
And in a sign of the furious efforts in Washington, Mr. Sandoval revealed that he had been lobbied personally by President Trump in a phone call. Mr. Sandoval declined to discuss the specifics of their discussion, which he said took place after his high-profile announcement last month with Mr. Heller that both would oppose an earlier version of the Senate bill.
Several of Mr. Sandoval’s Republican colleagues, from states that expanded Medicaid programs under the Affordable Care Act, were even more definitive in their opposition.
Gov. Phil Scott of Vermont, who won election in November even as Hillary Clinton carried his state by more than 20 percentage points, said the bill could cripple the health care system in Vermont.
“We’ve expanded Medicaid, and even a small tweak could have a devastating impact on us as a state,” Mr. Scott said. “We’ve made great strides at protecting the most vulnerable and I believe, in its present form, this would not be good for Vermont.”
Gov. Matt Bevin of Kentucky, who first emerged as a Tea Party-inspired challenger to Senator Mitch McConnell, the majority leader, came at the bill from the right. He sharply criticized his party’s decision not to eliminate a pair of taxes on high earners in the latest version of the bill.
“They’re going to lose as many votes as they’re getting,” Mr. Bevin said of the decision to keep the levies imposed by the Affordable Care Act. There was, he said, an “understanding that those two taxes were going to be gone.”
The governors have been playing an outsize role in shaping the congressional debate, with Republicans from states that expanded Medicaid often supplying the loudest voices. But some of the statehouse advice has plainly started to grate on Republican members of Congress.
“I don’t want to be irreverent, but, you know, people talk about their governors back home, are you kidding me?” said Senator Bob Corker of Tennessee. “I mean, if we can’t even deal with our governors back home, how will we ever deal with Medicare and Social Security?”
Every governor, Mr. Corker claimed, “would love for us to send free, unpaid-for money back home.”
Mr. Pence was notably more diplomatic as he spoke to the governors on Friday afternoon. He acknowledged the deep reservations in the room but branded the Senate bill a “rescue” measure. Mr. Pence detailed problems with the Affordable Care Act in Wisconsin and Ohio, two states where Republican governors have criticized the bill — and a pair of Republican senators, Mr. Johnson and Rob Portman, are wavering.
Mr. Pence, who as Indiana’s governor accepted federal funding to expand Medicaid, also acknowledged that the proposal would significantly change the population that receives health care coverage through the program. He insisted that the bill would hold Medicaid to its “original purpose” of covering the most severely vulnerable people and said too many “able-bodied adults” relied on the program.
The shift, he said, was aimed at “ensuring for the long run that Medicaid will be there for the neediest.”
“I really believe, as the president does, that we’re saving Medicaid,” Mr. Pence said.
It is unclear that such arguments are likely to move governors like Mr. Sandoval, who have resisted any pullback of Medicaid coverage.
And in a gentle gibe, Gov. Terry McAuliffe of Virginia, a Democrat who is chairman of the National Governors Association, noted in introductory remarks that Mr. Pence had been glad to take Medicaid funding when he was a governor.
“He showed true backbone himself in Indiana,” Mr. McAuliffe said, “when he expanded Medicaid for his citizens.”
Among Democratic governors, opposition to the legislation was unanimous and fierce, and party leaders declared anew on Friday that Democrats would pummel any Republican who dared support the bill in the more than three dozen governors elections unfolding over the next year and a half.
Gov. Dannel P. Malloy of Connecticut, the chairman of the Democratic Governors’ Association, accused Republicans in scorching language of being willing to let “people die in your state because they’re no longer eligible for health care.”
Other Democrats took a gentler approach, coaxing Republican senators from their states with do-the-right-thing appeals. Gov. John Bel Edwards of Louisiana invoked Mr. Cassidy’s years of work as a doctor in their state’s charity hospitals.
“They’re not just constituents that he and I have in common; these are the same people that he spent his adult life taking care of, and he knows how important it is for them to have meaningful access to quality health care,” Mr. Edwards said.
Gov. John Hickenlooper of Colorado, a Democrat, said he hoped his state’s Republican senator, Cory Gardner, would listen to his better angels and oppose the bill, calling Mr. Gardner “a compassionate and smart person.”
Mr. Hickenlooper, while saying he had no specific plans for the future, also declined to quash recent murmurs in Democratic political circles that he might challenge Mr. Gardner for re-election in 2020 if the senator votes in favor of the bill.
“This is something that matters a lot to me,” he warned.
What many Republicans fear is that action on what they have long derided as Obamacare also matters a great deal to their base. Failing to find consensus and act could prove just as risky politically, some here said.
“I do have concerns when Republicans have the House, the Senate, the presidency and 33 governorships across the country if we don’t govern,” Gov. Doug Ducey of Arizona said. “I think it’s time to lead and govern.”