Further complicating the matter are the four conservative Republicans — Rand Paul of Kentucky, Ted Cruz of Texas, Mike Lee of Utah and Ron Johnson of Wisconsin — who have already declared that they cannot support the health bill without changes to make it even more frugal. That put Senate leaders on notice that any move to placate the Dean Hellers of the Senate might only alienate other lawmakers still further.

Mr. McConnell continues to project confidence, even as the enthusiasm for the bill is largely muted. “I’m pleased that we were able to arrive at a draft that incorporates input from so many different members who represent so many different constituents who are facing so many different challenges,” Mr. McConnell said last week. He added: “There will be ample time to analyze, discuss and provide thoughts before legislation comes to the floor. And I hope every senator takes that opportunity.”

In fact, on the day last week that the bill was rolled out, Mr. Heller posted on Twitter a photo of himself sitting in an ornate chair plowing through it, a considerable feat of reading given the arcana of the bill’s statutory language. But in spite of his earnest decoding of phrases like the “applicable median cost benchmark plan,” what Nevadans have to say will probably have more impact — especially Mr. Sandoval, the most popular public official in the state, to whom Mr. Heller owes much.

The governor appointed Mr. Heller to the Senate seat in 2011 after the resignation of fellow Republican John Ensign and supported him during his successful run for a full term in 2012.

“Here is one thing that people don’t talk about a lot with Heller: He doesn’t like the job,” said Jon Ralston, editor of the Nevada Independent, a nonprofit news organization. “He was planning to run for governor.’’

But Adam Paul Laxalt, the current Nevada attorney general, the grandson of former Senator Paul Laxalt of Nevada and the son of former Senator Pete Domenici of New Mexico — is widely expected to run and has more or less pushed Mr. Heller out of the way.

Mr. Heller has never been the sort of rainmaker for the state that Senator Harry Reid of Nevada, the Senate minority leader from 2015 until early this year, was. Nor has he been a legislative leader. “The bottom line with Nevadans historically had been if you took care of the home issues, then how you voted in D.C. on the other stuff was less important,” said Michael Green, an associate professor of history at the University of Nevada, Las Vegas.