The mass vaccination sites open around Massachusetts had a "very good week" last week and Gov. Charlie Baker predicted Monday morning that those efforts are "gonna have a very good week this week too," despite a winter storm that could blanket the state in more than a foot of snow Monday into Tuesday.

As Baker gave a winter storm update from the State House, workers at the sites in Springfield, Foxborough and Boston were hustling to get to as many of the scheduled COVID-19 vaccine appointments as possible before the heavy snow picked up. Monday is the first day that people at the front of Phase 2 of the state's vaccine distribution plan -- most notably residents who are 75 years or older -- can get the first dose of the vaccine.

Baker said organizers of the mass vaccination site that opened Monday at Fenway Park encouraged people with Monday appointments to show up at any time during the day, the earlier the better, to try to get as many shots in arms before the snow picks up and possibly forces the site to close.

"I think the big goal for the mass vax sites is going to be to try to get as many of the folks who are scheduled today through -- and they've been talking to people all morning about that -- and folks who either are nervous about traveling given the storm and all the rest, they will do what they can to get them rescheduled this week," the governor said.

The Department of Transportation is coordinating with the mass vaccination sites at Fenway Park, Gillette Stadium in Foxborough and the Eastfield Mall in Springfield and other vaccine clinics to "help clear snow at these sites to keep them as accessible as possible for as long as possible," Baker said.

Information on vaccination site closures, changes in hours or changes to scheduled appointments would come directly from the health care provider running the site, Baker said.

Another mass vaccination site in Boston, this one at the Reggie Lewis Center in Roxbury, did not open Monday due to the coming snowstorm and everyone who was scheduled to get the COVID-19 vaccine there Monday has automatically been rescheduled until next Monday, Feb. 8, the city of Boston said.

The governor said vaccination sites large and small have received their weekly allocations of doses already and that the early week storm likely won't have a ripple effect on vaccination efforts later in the week.

"Most of the folks we talked to over the weekend feel pretty confident they'll be able to get through most of the people they were planning to get through this week," Baker said, adding that some health systems were planning to vaccinate eligible patients beginning Monday but might not start now until Wednesday "just because of some of the issues associated with transportation."

A good week for COVID-19 vaccination efforts might be just what Massachusetts needs as the vaccine become more available to more residents after the rocky early weeks of the rollout. As of Sunday morning, the federal government had distributed 1,060,900 doses of vaccine to Massachusetts and the state had administered 579,181 doses or about 55 percent, according to the U.S. Centers for Disease Control.

Alabama, Kansas, Missouri and Rhode Island are the only states to have administered a smaller percentage of the doses they had received, according to the New York Times. The Times' analysis of the CDC data showed that 6.7 percent of people in Massachusetts had received at least one dose of a COVID-19 vaccine, putting the Bay State in 40th place out of the 50 states.

The only states trailing Massachusetts are Nevada, Texas, Tennessee, Rhode Island, Kansas, Illinois, Alabama, Iowa, Missouri and Idaho.

The National Weather Service is forecasting that heavy snow will overtake most of the state by Monday afternoon and Baker said he is expecting "a pretty big dump somewhere between 12 and 18 inches of heavy wet snow across a lot of Massachusetts" by Tuesday afternoon.

A year or more ago, a snowstorm like the one moving in Monday afternoon would have been a lot more concerning since many people would leave work early and would have hit the roads at the same time that the storm was picking up and as MassDOT was putting its plows, sanders and other equipment into use.

"I'm going back now more than 10 years to that storm where we ended up with hundreds of cars that got stranded on -- they ran out of gas or they just couldn't go anywhere -- on the Turnpike, on 128 and on 495. It was just this incredible cluster of automobiles and people leaving work and all the plows landing at exactly the same moment exactly as the storm really picked up in the afternoon," Baker said. "We're not that worried about that happening today because the number of people who have the ability to work from home, the number of kids who are going to school remotely -- it's just a very different kind of logistics exercise than it would be under what we think of as sort of pre-pandemic circumstances."

Baker said he expects "most parts of Massachusetts are going to be in pretty good shape" by Tuesday night.