WASHINGTON  Peeling off his latex gloves after treating a 4-year-old boy having a severe asthma attack, J. R. Muyleart sighed with a touch of frustration. It was 3 a.m. and in the past 24-hour shift, Mr. Muyleart, a firefighter, had responded to at least one emergency call per hour.

But only two of those calls were for fires; most of the others involved heart attacks, diabetic sores, epileptic seizures and people complaining of shortness of breath.

“I joined the force to battle blazes, not to be an emergency room doctor,” Mr. Muyleart, 35, said as he and the rest of Engine Company 10 drove back to their firehouse, which for most of the last 15 years has been the busiest in the country, according to industry surveys.

Among the hidden costs of the health care crisis is the burden that fire departments across the country are facing as firefighters, much like emergency room doctors, are increasingly serving as primary care providers.