Approximately 45% of families currently in the Massachusetts emergency shelter system are migrant families — an amount Gov. Maura Healey said is untenable moving forward.

“We're at capacity and ... we simply cannot sustainably continue to house the numbers that we're seeing come into Massachusetts,” Healey said during Boston Public Radio’s "Ask the Governor" segment on Tuesday.

In response to a question from co-host Margery Eagen, Healey said it’s important that migrants are authorized to work, and said over 3,000 people have received work authorization or are in the process of getting permits. The governor also announced Monday that residents at state overflow sites will need to reapply every month to maintain their eligibility and prove that they are engaging with case managers and seeking work authorizations.

“We need to have these kinds of requirements imposed and guardrails so that we’re more quickly able to get people on the right track — and hopefully, Margery, diverted from longer-term emergency shelter stays,” she said.

In addition to capacity limits, which Healey set at 7,500 families, the governor says shelters face a fiscal challenge. Earlier this month, the Massachusetts Senate passed a spending bill that puts $245 million toward the emergency family shelter system.

“It is outrageous that we, as states, are having to bear the burden of this, bear the cost, bear the strain simply because Congress has failed to act,” she said.

Healey said the federal government’s choice to let in migrant families is why federal officials need to support the commonwealth, both with funding and in practice to speed up individuals’ work authorizations.

Last week, Florida Gov. Ron DeSantis threatened to send Haitian migrants to Martha’s Vineyard by plane, which would mimic a similar move he made in sending 50 mostly Venezuelan migrants to the island in 2022.

Healey said she doesn’t want to “play politics” and that Republicans like DeSantis should call on Republicans in Congress to pass the bipartisan immigration reform bill, which failed in the Senate.

“That would have resolved this a long time ago, including getting funding to states like Massachusetts that are having to bear the cost of this,” Healey said.

Also during her Boston Public Radio appearance, Healey addressed questions about her privacy and personal life. Last Friday, she revealed that she’d traveled to Puerto Rico for a vacation with her partner. Initially, though, she did not disclose where she’d gone, citing the need to balance security and privacy.

“My girlfriend took me away for my birthday for the weekend. I didn't think it was a big deal,” she said.

Healey also said she decided to reveal where she traveled because she didn’t want there to be more concern about where she was.

“Going forward, to be clear, I'll make sure that people know where I've been once I return,” Healey said. She said this protocol of revealing travel after the fact is consistent with governors in other states, and is what she’s been advised “in terms of security.”