Updated 8:44 PM ET

CHICAGO Patients can refuse a flu shot. Should doctors and nurses have that right, too? That is the thorny question surfacing as U.S. hospitals increasingly crack down on employees who won't get flu shots, with some workers losing their jobs over their refusal.

"Where does it say that I am no longer a patient if I'm a nurse," wondered Carrie Calhoun, a longtime critical care nurse in suburban Chicago who was fired last month after she refused a flu shot.

Hospitals' get-tougher measures coincide with an earlier-than-usual flu season hitting harder than in recent mild seasons. Flu is widespread in most states, and at least 20 children have died.

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Most doctors and nurses do get flu shots. But in the past two months, at least 15 nurses and other hospital staffers in four states have been fired for refusing, and several others have resigned, according to affected workers, hospital authorities and published reports.

In Rhode Island, one of three states with tough penalties behind a mandatory vaccine policy for health care workers, more than 1,000 workers recently signed a petition opposing the policy, according to a labor union that has filed suit to end the regulation.

Why would people whose job is to protect sick patients refuse a flu shot? The reasons vary: allergies to flu vaccine, which are rare; religious objections; and skepticism about whether vaccinating health workers will prevent flu in patients.

Dr. Carolyn Bridges, associate director for adult immunization at the federal Centers for Disease Control and Prevention, says the strongest evidence is from studies in nursing homes, linking flu vaccination among health care workers with fewer patient deaths from all causes.

"We would all like to see stronger data," she said. But other evidence shows flu vaccination "significantly decreases" flu cases, she said. "It should work the same in a health care worker versus somebody out in the community."

Cancer nurse Joyce Gingerich is among the skeptics and says her decision to avoid the shot is mostly "a personal thing." She's among seven employees at IU Health Goshen Hospital in northern Indiana who were recently fired for refusing flu shots. Gingerich said she gets other vaccinations but thinks it should be a choice. She opposes "the injustice of being forced to put something in my body."

Medical ethicist Art Caplan says health care workers' ethical obligation to protect patients trumps their individual rights.

"If you don't want to do it, you shouldn't work in that environment," said Caplan, medical ethics chief at New York University's Langone Medical Center. "Patients should demand that their health care provider gets flu shots  and they should ask them."

For some people, flu causes only mild symptoms. But it can also lead to pneumonia, and there are thousands of hospitalizations and deaths each year. The number of deaths has varied in recent decades from about 3,000 to 49,000.

A survey by CDC researchers found that in 2011, more than 400 U.S. hospitals required flu vaccinations for their employees and 29 hospitals fired unvaccinated employees.

At Calhoun's hospital, Alexian Brothers Medical Center in Elk Grove Village, Ill., unvaccinated workers granted exemptions must wear masks and tell patients, "I'm wearing the mask for your safety," Calhoun says. She says that's discriminatory and may make patients want to avoid "the dirty nurse" with the mask.

The hospital justified its vaccination policy in an email, citing the CDC's warning that this year's flu outbreak was "expected to be among the worst in a decade" and noted that Illinois has already been hit especially hard. The mandatory vaccine policy "is consistent with our health system's mission to provide the safest environment possible."

The government recommends flu shots for nearly everyone, starting at age 6 months. Vaccination rates among the general public are generally lower than among health care workers.