The proposal is one of several dramatic changes Healey’s administration will introduce — or try to introduce — in the coming weeks and months. State officials said Friday they intend to “phase out” the use of hotels and motels to shelter homeless families, a task that turned out to be a years-long effort for Healey’s predecessor. Healey said she will also ask lawmakers to increase subsidies for families looking for long-term housing to help move more of them out of shelter.

More immediately, state officials said they are creating a new two-track system for eligible homeless and migrant families seeking shelter. Starting December 10, many families will be allowed to stay for 30 working days in so-called temporary relief centers; they are currently limited to five dayswhich critics have argued is “cruel” and has helped push families to the street.

The state had previously had one 30-day flood protection limitplaces that served as precursors to the temporary relief centers.

Families considered high-risk, such as women who are late in pregnancy or families that include people with intellectual or developmental disabilities, will be allowed to stay for months in what state officials called a long-term track.

Exactly how long they would be allowed to stay could change. The legislature passed a law in the spring set a nine-month limit on most homeless families, but state officials say they want to lower the cap to six months, which would require approval from lawmakers. State officials also want to change the criteria used to determine when a family is granted an extension, which currently can go to veterans, single parents or others.

There are more than 7,000 families in the shelter system, according to government data. As of last week, 234 were in respite centers.

“We want to be clear with families: We’re looking for six (months) so nobody feels like they don’t have the right expectations,” said Lt. Gov. Kim Driscoll said in a phone interview Friday. “We think six months is possible. I reckon if people can find housing sooner than six months, they’ll take it.

Under the new system, families will not be able to choose between shelter tracks they enter, and those given access to “intensive services” at a temporary drop-in center will not be eligible for placement in longer-term shelters, officials said.

Driscoll said she did not have a projection of how much the various changes could reduce costs, but said the administration aims to eventually cap costs at $350 million a year.

The proposed changes are based on broad recommendations a state commission was made earlier this week, including to reduce the state’s reliance on hotels and motels for shelter and make the system more “fiscally sustainable.” Driscoll, who chaired the commission, said the state’s current approach is “not sustainable,” with costs projected to reach $1.09 billion this fiscal year.

Aides to House Speaker Ron Mariano and Senate President Karen E. Spilka said Friday they will review any bills Healey files. “The House has consistently been open to discussions about how to ensure that the shelter system can remain viable in the long term,” said Max Ratner, a spokesman for Mariano.

Gray Milkowski, a spokesperson for Spilka, said the chamber is “proud of how the state has confronted a humanitarian crisis with both empathy and fiscal prudence.”

The proposal stunned some advocates. Andrea Park, a staff attorney at the Massachusetts Law Reform Institute, said the current nine-month limit is already too little time for some families, and that families cannot be eligible for long-term protection once they are on the short-term track is a “very fundamental change” without legislative intervention.

“This says there is a category of people who are (shelter) eligible, but they’re not eligible enough. That’s potentially problematic,” Park said. “Every change that’s happened has been about limiting time, limiting access. We have not seen many details about the support” families receive.

Driscoll said the separate goal of phasing out the use of hotels would span both this fiscal year and the next. Currently, the state houses families in 56 hotels or motels, she said, and “our goal is to go one by one.”

“It really depends on how quickly our team can find housing” for families, she said.

Healey’s predecessor, Charlie Baker, similarly moved to wean the system off using hotels and motels. His administration steadily reduced the number of families living in them, from 1,500 in 2015 to only a few dozen in the fall of 2018, when Baker won re-election. Then, as more migrant families entered Massachusetts, the number began to climb again as Baker prepared to leave office last year.

The state is facing a much bigger challenge now. More than twice as many families — 3,369 — were in hotels as of Thursday, according to state data, and Massachusetts’ housing crisis has only intensified in the decade since Baker first took office.

Phasing out hotels as residences is “an important goal and I support the goal. But what we are experiencing here is a major crisis in housing for the whole of the Commonwealth, for everyone. And the housing crisis has only become more acute, says Jeffrey Thielman, CEO of the non-profit migrant aid organization International Institute of New England. Staying in hotels “should be very short term – in a perfect world.”

The state will need the Legislature to approve hundreds of millions more this fiscal year for the shelter system, officials have said. Healey intends to file an additional spending bill that would require more money for the rest of the fiscal year, as well as proposing that the rental subsidy families can receive under the state’s HomeBase program increase from $15,000 per family per year to $25,000 per family per year.

HomeBASE is currently designed to match homeless families with landlords who have vacant apartments, then subsidize rent and other expenses for up to three years. But in exchange for a higher grant, Healey wants to limit the benefit to two years instead of three, to “manage expectations” as the state tries to funnel families into permanent housing, according to her administration.

The program is seen as a key part of helping to find long-term housing, but advocates have said it is also backed up and burdened with red tape, meaning some applicants miss out on available apartments, The Globe has reported that.

In a statement, Healey touted improvements in a system that for most of the past two years has been overwhelmed, including by migrant families entering the state. Currently, approximately 7,100 families are in shelters, with an average of 15 to 18 families seeking shelter each day. But that’s a steep decline from the up to 40 families who sought shelter per day at its peak, according to Healey administration officials. Currently, about 65 percent of families in the system are considered “long-term residents of Massachusetts.”

Healey said that “the size of the system has been stable over the past year.”

Still, “more must be done so that Massachusetts taxpayers do not continue to be on the hook for this federal problem,” Healey said in a statement.

Matt Stout can be reached at [email protected]. Follow him @mattpstout.