What angered the Republican rank and file about Mr. Heller’s critique was not so much his unease with the compromise Senate legislation — a measure that many on the far right are also displeased with — but that he would so purposefully undermine the president’s agenda.

And it is not just party activists who are displeased with the senator.

Mr. Adelson and Mr. Wynn, two of Las Vegas’s leading gambling titans, each contacted Mr. Heller at the request of the White House last week to complain about his opposition to the Republican-written health overhaul, according to multiple Republican officials.