BOSTON (NEWSnet/AP) — The number of homeless families seeking emergency shelter in Massachusetts is nearing a 7,500-family threshold, and Gov. Maura Healey says the state no longer can accommodate them and will place families on a waiting list.

Healey has said she doesn’t want to see families without homes, but the state essentially has reached its shelter capacity. The spike in demand is being driven in part by a surge of migrant families entering the state.

Critics argue Healey’s decision to cap shelter placements violates the state’s “right-to-shelter” law. Massachusetts is legally required to provide emergency shelter to eligible families.

Under Healey’s plan, women, young children and those with acute medical needs and health issues are given priority. The state is considering limiting how long a family can stay at a shelter, Healey said.

On Tuesday, Healey announced a $5 million grant program to help local organizations create overnight shelter for families and pregnant women with no other options.

Massachusetts lawmakers are considering a bill to secure $50 million to establish one or more locations where homeless families can find temporary refuge while they wait for shelter space.

House Speaker Ronald Mariano said that could be a single large site like  Hynes Convention Center in Boston or smaller sites throughout the state.

Denying families emergency shelter could force some into unsafe living conditions, said Kelly Turley, director of the Massachusetts Coalition for the Homeless.

She and other homeless advocates have pressed the Legislature to approve money for a large living site similar to that described by Mariano.

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