BOSTON (AP) — A Superior Court judge on Wednesday denied a request by lawyers representing homeless families in Massachusetts to temporarily bar the state from capping the number of families offered emergency shelter.

The ruling helps clear the way for Democratic Gov. Maura Healey to institute the new policy. Healey has said the cap will kick in when the number of families hit 7,500. At that point the state will create a waitlist. Those with the highest needs will be prioritized, Healey said.

As of Wednesday, the state reported 7,388 families were enrolled in the state’s emergency shelter system, with 33 families enrolled just in the prior 24 hours. Healey has said about 40 to 50 new families are requesting shelter each day and that an influx of migrants is driving the spike in demand.

Critics say Healey’s plan violates the state’s “right-to-shelter” law. Under the law, Massachusetts is legally required to provide shelter to eligible families through the emergency assistance program.

Lawyers for Civil Rights, a nonprofit based in Boston, filed the class-action lawsuit on behalf of three families on the brink of homelessness, arguing that Healey’s changes are being rushed into place without any public process or required notice to the Legislature.

Jacob Love, an attorney with the nonprofit, said in court Tuesday that the proposed waitlist of homeless families is akin to a fire department “creating a waitlist for families with ongoing house fires.”

When the Legislature funded the program, it required the agency in charge — the Executive Office of Housing and Livable Communities — to give lawmakers about three months notice of any changes in case they wanted to intervene, lawyers for the group argued.

In her ruling Wednesday, Judge Debra Squires-Lee said that under the guise of requiring the administration to notify the Legislature, she didn’t have the authority to prohibit the administration from exercising its discretionary authority to manage the emergency assistance program.

Healey said the state isn’t abandoning the right-to-shelter law but has to deal with shrinking shelter capacity.

“We do not have the shelter space, the physical space. We do not have the number of shelter providers and service providers to be able to withstand this capacity and we don’t have the funding,” Healey said Tuesday on WBUR.

The Healey administration filed proposed regulations Tuesday about the proposed cap, including letting state officials limit how long a family could stay in a shelter. Housing advocates have said families have had to stay in shelter on average a year or more.

Kelly Turley, director of the Massachusetts Coalition for the Homeless, warned that capping the number of families seeking shelter could force some into unsafe living conditions.

“We haven’t seen a large number of families staying in places like the Boston Common because we’ve had the right to shelter but we’re afraid as winter approaches that we will see more families staying in very unsafe places if the state doesn’t guarantee the right to shelter,” she said after Tuesday’s hearing.

Healey has asked lawmakers to approve up to $250 million in additional state money to help cope with the demand.

Democratic Massachusetts House Speaker Ronald Mariano has said the House continues to evaluate the need for additional funding but has no plans to change the 1983 shelter law.

Families are spread out across hundreds of locations in 90 cities and towns in a range of facilities, from traditional shelters to temporary sites like college dorms.