With so many hospitals facing the same problems, the elasticity in the health care system is gone. Hospitals that fill up cannot count on being able to transfer patients elsewhere, and medical workers are being run ragged.

“There is not a lot of wiggle room,” said Loy Howard, president of the Tanner Health System. “I have been doing this for 35 years, and I have not seen this kind of wear and tear on the staff.”

Hospitals in cities large and small are running short of intensive care beds. In El Paso, just 13 of the 400 intensive care beds were unoccupied last week. In Fargo, N.D., there were just three. In Albuquerque, there were zero.

In all, more than one-third of Americans live in areas where hospitals are running critically short of intensive care beds. Hospitals serving more than 100 million Americans reported having fewer than 15 percent of intensive care beds still available as of last week, according to a New York Times analysis of the federal data released on Monday.