The recommendation Friday would eliminate even more people from the pool of potential vaccinees at a time when the government is trying to increase its numbers.
Two states, New York and Illinois, temporarily suspended their programs while questions about the link to heart disease are investigated.
To date, 17 recipients of the vaccine have suffered heart problems afterward, and federal health officials are looking for a possible link to the vaccine. Three people have died, including a 55-year-old National Guardsman that the Pentagon announced Friday.
The man's death is the first in a mandatory military inoculation program that has vaccinated 350,000 people. The other two deaths were of health care workers in private hospitals.
Federal officials had planned to offer the vaccine on a voluntary basis to at least 450,000 civilians in the program's first month. After two months, only about 25,000 have been vaccinated, with many hospitals opting out of the program.
The Centers for Disease Control and Prevention is working to improve the numbers, but after learning of the first death, officials decided anyone with a history of heart disease should not get the vaccine. The Pentagon adopted the same policy Friday.
On Friday, an advisory committee recommended the CDC go beyond people already sick with heart disease to those at risk. The Advisory Committee on Immunization Practices suggested the shot not be given to anyone with at least three risk factors for heart disease, such as smoking, high blood pressure and diabetes.
But preventing heart problems among people vaccinated is not easy.
Experts 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.
All three heart attack victims had risk factors for heart disease. The Guardsman, who died Wednesday after a heart attack a day earlier, smoked and had high cholesterol, and an autopsy showed that he had had coronary disease, the Pentagon said.
If it adopts the panel's recommendation, the CDC estimates it that would exclude about 6 percent of health care workers and 10 percent of the general public.
The vaccine is made with a live virus that can cause illness of its own. Certain people are already known to be at particular risk for vaccine side effects, and have always been excluded from the program. That includes people with compromised immune systems such as organ transplant recipients, pregnant women and those with a history of skin problems.
The CDC panel had considered a more drastic step: Excluding anyone over the age of 50. But members worried that would essentially kill the program.
Still, at least one member of the panel want to go even further and suspend all vaccinations while the heart question is investigated.
"There still hasn't been a case of smallpox anywhere in the world," said Dr. Paul Offit of The Children's Hospital of Philadelphia.
"There are a lot of people who have heart problems and may not know it," he said, suggesting that the screening system might not find everyone at risk.
No matter what the recommendation, news of the deaths is likely to make health care workers even more wary of the vaccine, said Dr. Deborah Kamali of the University of California, San Francisco, who helped organize area doctors to write the CDC and urge that the program be halted.
She and her colleagues argue that known risks of the vaccine outweigh the unknown risks of an attack with smallpox, which was wiped from the Earth more than two decades ago.
"I think it will definitely make health care workers more reluctant. This is something they can relate to," she said. "As a field, we've already been reluctant."
By Laura Meckler