BOSTON — For Mark DeJoie, the head of North Shore human services provider Centerboard, Inc., the need to limit the number of people in the state’s emergency shelter system boils down to a simple “math problem.”

“There’s just too many people for too few units. And that, too, has been exacerbated because of the migrant influx,” he said in an interview. “We’re dealing with an immigration crisis as a shelter system. We’re not built for that. We’re built to house families.”

An influx of migrants over the past year has pushed a shelter system built to handle about 3,000 families each year to its limits, forcing providers across the state to scramble to find additional housing units for the thousands of new arrivals that have made their way to Massachusetts.

More than 1,500 families have entered the emergency shelter system since Gov. Maura Healey declared a state of emergency at the start of August. The Executive Office of Housing and Livable Communities reported 7,089 families in the system as of Friday, with 3,624 at traditional sites, 3,376 living in hotels and motels, and 89 at temporary sites.

Many, including Healey, other providers, and advocates, have described the scenario as unsustainable without assistance from the federal government and as costing the state tens of millions in taxpayer dollars, at least, each month.

It led Healey this past week to limit the number of families that can stay in the system to 7,500, a move that will surely test the boundaries of Massachusetts’ right-to-shelter law, which requires the state to temporarily house homeless families with children and pregnant women. Healey argued the state has neither the money, space, nor personnel to keep expanding the system.

For a handful of shelter providers who say they were feeling strained months ago, putting a cap on the number of families in the emergency shelter system was inevitable. Still, others are worried what will happen to those who arrive in the state once all the space is taken up.

“We are grateful for the administration’s all-hands-on-deck approach to the (emergency assistance) shelter crisis since taking office, but fear that the announced changes may result in children and families being unable to access shelter when it is needed the most,” a trio of housing policy and law groups said in a Friday statement.

The logistics of housing a never ending stream of migrants arriving in states across the country — most who fled unstable and dangerous conditions at home and made a treacherous journey to reach the United States — have vexed Democratic governors and mayors this year in places like New York City and Chicago.

Healey is no exception.

What started as an apparent political stunt with tens of migrants landing on Martha’s Vineyard last year at the behest of Florida Gov. Ron DeSantis, just before Healey took office, has turned into a very real problem for Massachusetts and emerged as one of the first tests of the Healey administration.

The Healey administration and some providers say part of the answer to reducing the number of families in the system is access to work training and federal authorizations that will allow them to secure jobs.

The Central Massachusetts Housing Alliance, a service provider based in Worcester, was at capacity in July and has doubled shelter capacity since November 2022, said Executive Director Leah Bradley.

The organization continues to hire staff “and do the things that we need to do, but we just can’t keep up,” Bradley said.

“It’s really a federal issue that needs some federal intervention,” Bradley said in an interview. “The folks that are coming here are lawfully here, and the federal government has said that they’re allowed to be here so it really is something that we just need the federal government to partner with us on this.”

It is anybody’s guess as to whether the federal government will send more direct aid to Massachusetts, though the Biden administration has said it is attempting to reduce the time it takes to process applications for work authorizations and sent a Department of Homeland Security team to Boston this month.

Healey on Friday applauded a $1.4 billion funding request for a shelter and services program run by the Department of Homeland Security, which handed Boston and the state $1.9 million earlier this year to expand shelter and transportation services for migrants.

“More funds from the state government, and particularly the federal government, will enable us to provide job training, (English as a second language) training, and provide the opportunity for people to move out of the emergency shelter system, out of motels into apartments so they can become a part of our thriving economy,” said Cindy Rowe, president and CEO of the Jewish Alliance for Law and Social Action.

But money alone will not fix the issues Massachusetts’ emergency shelter system faces, said DeJoie, the head of Lynn-based Centerboard, Inc. The problem is lack of space and ability for migrant families to quickly find work, build a source of income, and exit the system, he said.

“Quite frankly, the people that are here, we could use them,” DeJoie said. “I would hire some of the people that are living in our shelter just because the skills that they have, the translation services, the cooking abilities they have. But I can’t.”