“So very quickly, we start having more than 150 million doses a month in March, April, May,” he added. He and other federal officials have said that the general public is likely to be able to be vaccinated by May or June.

The C.D.C. panel was originally not supposed to vote on its recommendations until after the F.D.A. had approved a vaccine. But it bumped up the timing to give states more guidance as they complete their distribution plans, which must be submitted to the C.D.C. on Friday.

On Tuesday, the group specifically suggested that within the long-term-care population, residents of nursing homes, who tend to be the most frail and susceptible to Covid, should get the first vaccines in the event that there aren’t enough, along with staff members who have not had the virus within the last 90 days.

Within the much larger category of health care workers, the panel said that health systems should consider prioritizing those who have direct contact with patients and their families and those who handle infectious materials. Dr. Nancy Messonnier, who leads the C.D.C.’s National Center for Immunization and Respiratory Diseases, told the panel that based on her recent conversations with state health officials, most states and large cities “believe they can vaccinate all of their health care workers within three weeks.”

But whether they reach that goal depends on how much vaccine they get, and how quickly. Gov. Andy Beshear of Kentucky told reporters on Monday that his state had more than 200,000 health care workers but would receive only 38,000 doses in its first shipment and that it might not get another for two weeks.

Long-term-care facilities include nursing homes, with about 1.3 million residents; assisted-living facilities, with 800,000 residents; and residential care facilities, which tend to be small and cater to specific populations. The federal government has contracted with CVS and Walgreens to deliver vaccines to most such facilities nationwide, with teams of pharmacists making three visits to each to ensure that every staff member and resident gets both an initial shot and a booster shot several weeks later.

Several members of the panel urged that small community doctors’ offices not be left off the initial priority list. “Transmission dynamics suggest providers who care for patients earlier in their course of illness may be at higher risk,” said Dr. Jeffrey Duchin, a member of the panel who is in charge of public health in Seattle and King County, Wash.