“This is unlike anything I have ever seen,” Mr. Neidorff said. “They have to sit back and think through what they are doing.”

Within hours after the bipartisan group of governors sent their letter opposing the repeal bill, Senator Cassidy provided a letter from 15 Republican governors supporting the concept of “adequately funded block grants to the states.”

By Tuesday evening, Ms. Murkowski appeared to be the key vote.

At least two other Republican senators, Rand Paul of Kentucky and Susan Collins of Maine, are likely no votes. With Democrats united in opposition, Republican leaders cannot afford to lose any other votes.

Vice President Mike Pence met with Senate Republicans at lunch in the Capitol on Tuesday and told them the Trump administration was fully behind the repeal bill, which would send more than $1 trillion to states from 2020 to 2026.

After the lunch, Mr. Graham said, “I’ve never felt better about where we’re at.”

Mr. Graham said he had spoken to President Trump about the bill five times in the last two days, and said Mr. Trump was “focused like a laser” on it. Mr. Graham quoted Speaker Paul D. Ryan as saying that the House would pass the bill if the Senate approved it.

The Graham-Cassidy bill would blow up the architecture of the Affordable Care Act, a striking departure from the Alexander-Murray effort to draft a modest bipartisan bill to provide federal funds to insurance companies to reimburse them for reducing out-of-pocket costs for low-income consumers.

Some conservatives argued that the bipartisan bill would just prop up the health law.

It “doesn’t have a chance in the House,” said Senator Ron Johnson, Republican of Wisconsin, who helped write the Graham-Cassidy bill.