GOV. MAURA HEALEY tried to have it both ways on the state’s right to shelter law Monday, insisting her administration is not backing away from requirements of the law while acknowledging that shelter capacity will max out by the end of this month and after that placements in the program will not be guaranteed.

The governor said 7,000 families, roughly 23,000 people, are in the emergency shelter system now – half of them new arrivals from outside the country and half of them children. She said the program is expected to reach capacity at 7,500 families, or 24,000 people, by the end of the month.

“We are not ending the right to shelter law,” she said. “We are being very clear, though, that we are not going to be able to guarantee placement to those who are sent here after the end of this month.”

The right to shelter law guarantees shelter to any family or pregnant woman in Massachusetts without access to housing.

The governor said her administration will be taking a number of steps to move people out of the shelter system as quickly as possible to make room for others, but she said shelter cannot be guaranteed after the state reaches its capacity level. She said new arrivals at that point will be triaged, with those in the most dire need helped first while others will be placed on a waiting list.

The whole notion of a capacity limit hasn’t been broached before, but the unusually rapid growth in the system, driven by new arrivals from foreign countries, prompted Healey to say the state can only do so much. She first declared a state of emergency on August 8, when there were nearly 5,600 families, or roughly 20,000 individuals, in the shelter system.

“This level of growth is not sustainable,” Healey said at a press conference at the State House.

“We need everyone to understand that we are entering a new phase of this shelter challenge,” Healey said. “Massachusetts will continue to rise to this challenge. That’s who we are. But I want there to be no doubt, this is a federal problem that demands a federal solution.”

The governor said the migrants flocking to Massachusetts are all here legally. “They are here lawfully, allowed in with the knowledge and consent of our federal government,” she said.

Rep. Peter Durant, a Republican from Spencer who is running for a vacant Senate seat, referred to the new arrivals from outside the country as illegal aliens. He said who is legal depends on the definition of legal. Many of those coming to Massachusetts cross the border into the US and then ask federal authorities for an asylum hearing, he said.

“Does that make you legal?” he asked. “Maybe, but I think that’s too cute by half.”

Durant has called for the right to shelter law to apply only to US citizens. He said Healey’s announcement doesn’t really address the root problem of the right to shelter law.

“The first step is to stop the flow of people coming in,” he said. “It’s completely irresponsible to say we’re at capacity but keep sending them here, keep coming.”

Healey was asked if her comment about shelter capacity was a signal to migrants to stop coming to the state. “It’s certainly a communication that we are reaching capacity and therefore don’t expect to be able to house people … in the existing infrastructure,” the governor said.

The governor once again pressed the federal government to provide more shelter for new arrivals in Massachusetts, to provide more money for states dealing with large migrant populations, to provide work authorizations more quickly for migrants, and to pass new immigration laws.

But she said the state can no longer just sit by and wait for the federal government to act. In addition to placing a cap on the shelter program and appointing retired Lt. Gen. Leon Scott Rice, who has 40 years of experience in the US Air Force and the Air National Guard, as emergency assistance director, Healey said the state is going to get more aggressive in moving people out of the shelter system.

She said one priority is moving long-term emergency shelter occupants (some have been in the system for more than a year) into housing.  She said her administration is also going to work with employers to move those in the shelter system who can legally work into jobs as quickly as possible. She said the state will also begin job training for those without work authorizations so they can be ready to take jobs once authorization is provided.

Healey didn’t respond to a question about how much the emergency shelter system will cost the state once it reaches capacity.  The shelter budget for the current fiscal year was originally set at $325 million to serve 4,700 families, but Healey in mid-September asked the Legislature for $250 million more to service an estimated 6,300 families. With the number of families in the program expected to rise to 7,500 in two weeks, more money will probably be needed.