Washington ? Three people have died of heart attacks after receiving the smallpox vaccine, and two states have suspended their programs, throwing a struggling campaign into even deeper trouble.

Health experts are investigating a possible link between the vaccine and heart problems that have occurred in 17 people, including the three fatalities. Two of those were health care workers in private hospitals. The third, announced Friday by the Pentagon, was a 55-year-old National Guardsman, the first death in a military inoculation program that has treated 350,000 people.

The civilian program, which unlike the military’s is voluntary, has moved much slower. Federal officials had aimed to offer the vaccine to at least 450,000 people in the program’s first month. After two months, only about 25,000 have been vaccinated, with many hospitals opting out of the program altogether.

Despite the low numbers, the Institute of Medicine recommended this week that federal officials consider whether they have vaccinated enough people to handle a terror attack using the smallpox virus, should one occur. Many states might discontinue their programs as they reconsider their readiness, said Dr. Brian Strom, the head of the Institute of Medicine’s smallpox committee, which is advising the Centers for Disease Control and Prevention on the program.

The recent deaths add weight to the recommendation, Strom said in an interview Friday.

“They’re going to have more trouble now” getting volunteers, he said. “I think people are going to be afraid.”

He predicted that questions about heart disease may also prompt states formally or informally to suspend their programs. Already, New York state and Illinois have temporarily suspended vaccinations while questions are sorted out about the possible link between heart disease and the vaccine.

At the CDC, officials are trying to figure out what changes are needed, given the possibility of a heart connection.

They believe the vaccine may be to blame for a dozen cases of people who have suffered heart inflammation, a relatively mild condition. But there is no way to screen out those who are at risk for it, so there is little they can do to prevent it.

There are known risk factors for heart attacks and angina, or chest pain, but experts are not convinced that these conditions are related to the vaccine. Four people who had been vaccinated suffered heart attacks, including the three who died, and two reported angina. Many Americans suffer from heart disease, so these could be coincidental.