“The folks who Hillary Clinton called the ‘deplorables’ are actually those who want better coverage, who we’d be hurting if we don’t change this bill,” Mr. Cassidy said, noting that Mr. Trump promised “he’d give them better care.”

The senator, a physician who once worked in his state’s charity hospital network, bluntly said that the philosophical debate was over and that his party ought to be pragmatic about how best to create a more cost-efficient and comprehensive health care system.

“There’s a widespread recognition that the federal government, Congress, has created the right for every American to have health care,” he said, warning that to throw people off their insurance or make coverage unaffordable would only shift costs back to taxpayers by burdening emergency rooms. “If you want to be fiscally responsible, then coverage is better than no coverage.”