Dr. Biron Baker runs a family medicine clinic in Bismarck, North Dakota. Every day patients walk through the door, and any number of them could be sick with the coronavirus. Baker treats them anyway, doing the best he can with his small staff to keep from getting sick.

But as the nation’s daily death counts from the coronavirus shatters previous records and the vaccine rolls out for front-line health workers across the country this week, Baker and his staff are so far not among those scheduled to receive it — and they do not know when their turn will come.

They have been given no information about the vaccine, he said, adding that he had tried several times to call state officials for an answer but with no luck. “No email, no fax announcement, nothing at all,” he said.

The vaccine is perhaps the only bright spot as the coronavirus continues its rampage around the country and new data shows a jobless crisis far worse than in other recessions. Still, in the scramble to vaccinate millions of health workers, difficult choices about who comes first — and who must wait — have started to surface. So far, the effort is concentrated in hospitals. Workers treating COVID-19 patients in intensive care units and in emergency departments have in recent days been beaming symbols of the virus’ demise.

But there are roughly 21 million health care workers in the United States, making up one of the country’s largest industries, and vaccinating everybody in the first wave would be impossible. That has left entire categories of workers — people who are also at risk for infection — wondering about their place in line.

“There’s a lot of nervous buzz and questioning going on,” said Arthur Caplan, a bioethics professor at NYU Grossman School of Medicine.

There are broad gray areas, he said: primary care doctors in areas with high infection rates, workers who handle bodies, firefighters who respond to 911 calls, dentists, pathologists who handle coronavirus samples in labs, hospice workers, chaplains.

“Right now, they are asking, ‘Where am I in all of this?’ That’s turned into quite a behind-the-scenes tussle.”

The Centers for Disease Control and Prevention has laid out categories but they are broad, so each state — and each hospital system — has come up with its own plan and priorities. The result has been a sometimes confusing constellation of rules and groupings that has left health care workers like Baker — as well as professional societies of groups such as pathologists, dentists and medical examiners — wondering where they stand.

“What’s happening is a little confusing,” said Dr. Sally Aiken, a medical examiner for Spokane County in Washington State and president of the National Association of Medical Examiners. “We are not really clear if we are somewhere in Phase 1A or not,” she said, referring to the CDC’s name for the first vaccination group. She noted that rules differed by state.

She voiced a view expressed by many who were interviewed for this article: “We don’t need to be at the top. But we are also trying to respectfully say, ‘Don’t forget about us. We have some risk, too.’ “

One of the most critical categories has been firefighters and other emergency services workers.

Firefighters, who respond to 911 calls and enter people’s homes, are often a first point of contact with the health care system. They provide about 85% of emergency medical response in the country, said Harold Schaitberger, general president of the International Association of Fire Fighters.

But despite their front-line role, he said, it is unclear when they will be vaccinated.

“We should be absolutely up front,” Schaitberger said. Firefighters had to fight to get access to adequate personal protective equipment, he said, and now they are having to do it all over again with the vaccine.

And as the virus surges in many places, that job has only gotten more dangerous. Last week, six of the 33 firefighters serving Newport, Kentucky, a city across the river from Cincinnati, were out of commission because they had either contracted COVID-19 or had close contact with someone who did.

Jake Silvati, president of the Newport Professional Firefighters Local No. 45, said he had not heard a clear answer from the office of Gov. Andy Beshear on where they will fall in line. He said he supported the governor, but he expressed worry that some people responsible for the vaccine rollout may not realize the crucial role that firefighters play.

“The sooner that we can get that vaccine, the higher we can get in line,” Silvati said. “It’s just another tool for us to be healthy.”

Hospitals are ground zero for the vaccine effort, but even there, not everyone can be covered with the first allotment.

Dr. Melanie Swift, a doctor at the Mayo Clinic, is helping that hospital system manage the effort to begin vaccinations of its large staff, mostly in the Midwest.

The system made a spreadsheet of risk categorizations for each of its 72,000 staff members, and the workers with the most frequent, intensive and least controlled contact with COVID-19 patients will be vaccinated first. The first doses of the vaccine, set to arrive this week, will probably cover most of those workers, Swift said, roughly 6,500 people in its flagship Rochester, Minnesota, location.

What other workers have asked when they will get it?

“Oh, only everyone,” she said. “Most people have prefaced their question with, ‘Of course I don’t think I should be ahead of the COVID ICU staff who have been drinking from a fire hose since March. But our pediatric patients don’t stay reliably masked; perhaps we are at increased risk,” she said, listing an example of one common question.

She said she had been telling people that everyone would eventually get vaccinated.

The question of when is a moving target. Dr. William Borden, chief quality and population health officer at G.W. Medical Faculty Associates in Washington, said that the doses it had received would not cover all of the workers in the top priority departments but that he hoped to receive more soon.