• Walgreens and CVS Health officials said they expect to have Covid-19 shots for the general public at their stores in the early spring.
• The two drugstore chains are playing a central role in an earlier phase of the rollout: Vaccinating staff and residents at tens of thousands of long-term care facilities, such as nursing homes.
• Rite Aid, Kroger, Publix and H-E-B — some of the other retailers involved in the vaccine effort — said they're still waiting to hear when they will receive vaccine doses and can begin offering the shots.

Health-care workers across the U.S. received Covid-19 vaccinations Monday, the first Americans to do so outside of a clinical trial. 

It will still be several months, however, before the average person can walk into their local drugstore or grocery store and receive the vaccine. In interviews with CNBC, Walgreens and CVS Health officials said they expect to give shots to the general public starting in the early spring.

"Over the next couple of months we anticipate that we'll be able to have [it in] our stores similar to the flu season," Rina Shah, group vice president of pharmacy operations at Walgreens, said Monday on CNBC's "The Exchange." She said that would be "hopefully in the spring timeframe."

For now, Shah said, it's important for health-care workers and long-term care facilities residents to take priority, because supplies remain limited.

"As more and more vaccine becomes available, access to that vaccine will continue to grow," she said.

Chris Cox, a senior vice president of CVS, said he hopes the company can give the vaccine at its drugstores "somewhere in the April/May timeframe."

Two prominent public health officials — Dr. Anthony Fauci, White House coronavirus advisor, and Dr. Ashish Jha, dean of Brown University School of Public Health — both said Monday that they expect healthy Americans who don't qualify for a vaccine due to their job or health condition to start getting the vaccine by late March or April. Fauci made the comments in an interview with NBC News' Hallie Jackson, and Jha shared the same timetable in an interview with ABC's "The View."

Nearly 20 drugstores and grocers — including Walgreens and CVS — partnered with the U.S. Department of Health and Human Services in mid-November to help administer Covid-19 vaccines. The two drugstore chains will also play a central role in an early phase of the vaccine rollout. They have deals with the federal government to vaccinate residents and staff at tens of thousands of nursing homes and other long-term care facilities across the country.

Costco also is assuming it will begin offering the general public Covid-19 vaccinations at its in-store pharmacies around early spring, CEO Craig Jelinek said Monday on CNBC's "Closing Bell."

Rite Aid, Kroger, Publix and H-E-B — some of the other retailers involved in the vaccine effort — said they're still waiting to hear when they will receive vaccine doses and can begin offering the shots to Americans.

Walmart is preparing its more than 5,000 stores for the vaccines, even though it did not say when they may arrive. In a post on the company's website, its chief medical officer Dr. Tom Van Gilder said the big-box retailer is adding freezer capacity and getting dry ice for its pharmacies. He said it's also developing a process to help people keep track of their first and second vaccine doses and educating employees who may receive them.

CVS' Cox said in an interview with CNBC last week that when vaccines are available for the general public, people will have to make appointments with CVS to get their shots.

"When someone makes their appointment, we're going to educate them right then and there that this is a two-shot vaccine and we're going to have them schedule it just like a round-trip plane ticket, where they're going to schedule both of their doses at the same time," said Cox, who also serves as the company's liaison to Operation Warp Speed, the Trump administration's vaccine development program.

The vaccine from Pfizer and BioNTech, which requires two doses, is the only one that has received emergency use authorization from the Food and Drug Administration so far. By the spring, however, public health officials anticipate vaccines from multiple manufacturers will be available. Moderna's vaccine could get the greenlight from the FDA later this week. It also requires two doses.

Cox said the vaccine the customer gets will depend on what's in stock at the store.