At the Kings Valley Diner in Mr. Faso’s district, stretching across the Catskills and north past Albany, the congressman won some harsh reviews. He had at first hesitated over the health care proposal, which the Congressional Budget Office projected would lead to 24 million fewer people having health insurance over a decade. But Republican leaders pursuing Mr. Faso shifted the cost of Medicaid programs away from upstate counties like the ones he represents, and he backed the bill days before it fell apart.

“Faso played that whole thing like an idiot, to be frank,” said Jim Palmatier, 62, who said he was disappointed to see the congressman horse-trading over a doomed bill. “He tried to be a little too clever, and he just ended up looking like a fool. There’s no way I’m voting for him next time around.”

Eating breakfast with his teenage grandson, Mr. Palmatier, who described himself as a conservative, said he wanted to see the Affordable Care Act repealed but had been disappointed with the Republicans’ replacement.

“They tried to get it through so quickly, they barely had time to explain the thing,” he said.

In Representative Adam Kinzinger’s district, a Republican seat in a largely rural area outside Chicago, even conservative voters voiced unease with Mr. Kinzinger and his party’s sputtering approach to health care. Bill Chivers, 64, a teacher in Onarga, Ill., who said he leaned Republican, questioned whether lawmakers understood the bill: “Nobody knew what it was. Not even Congress — they don’t even know what it means.”

Anthony McIntyre, 55, who was grilling pork burgers for a fund-raiser outside the Hometown Family Foods store in Gilman, Ill., said he was relieved that the bill had failed. Mr. McIntyre, who has health coverage through his job in roofing, said he feared that the bill would have led to higher insurance rates.