In Coudersport, Pa., a town in a mountainous region an hour’s drive from the nearest Walmart, Cole Memorial Hospital counts on two Jordanian physicians to keep its obstetrics unit open and is actively recruiting foreign specialists.

In Fargo, N.D., a gastroenterologist from Lebanon — who is among hundreds of foreign physicians in the state — has risen to become vice president of the North Dakota Medical Association.

In Great Falls, Mont., 60 percent of the doctors who specialize in hospital care at Benefis Health System, which serves about 230,000 people in 15 counties, are foreign doctors on work visas.

Small-town America relies on a steady flow of doctors from around the world to deliver babies, treat heart ailments and address its residents’ medical needs. But a recent, little-publicized decision by the government to alter the timetable for some visa applications is likely to delay the arrival of new foreign doctors, and is causing concern in the places that depend on them.