“The right to shelter law and the sanctuary city laws that have been imposed on the state by the State House and by the Supreme Court of Massachusetts create incentives that dig a hole that will never be filled,” said Lou Murray, chairman of Bostonians Against Sanctuary Cities.

A 1983 law makes Massachusetts the only state in the country that has a legal obligation to shelter unhoused families, which the state has always interpreted to include noncitizens living in the state.

About half of the residents of the Emergency Assistance shelter system are new immigrants, and the system’s dramatic growth by thousands of families in the last year has largely been driven by newly arriving families from other countries, as Massachusetts and the U.S. at large struggle with an immigration crisis.

“It’s a twist of the law, that it has to even let people that just come into the state for the sole purpose of shelter to use the right of shelter,” Murray said.

The protestors argued Wednesday that the shelter system was “totally overrunning our state budget,” and that ending the state’s right-to-shelter law would slow the wave of new arrivals.

Massachusetts’ emergency shelter costs will approach $1 billion annually this fiscal year and next fiscal year, according to Gov. Maura Healey’s administration.

“Tax dollars are a precious resource, and what is happening in Massachusetts is entirely unsustainable,” said Henry Barbaro, executive director of the Massachusetts Coalition for Immigration Reform. “I think that there are plenty of poor and needy Americans that should come first.”

House Ways and Means Committee Chair Rep. Aaron Michlewitz earlier this week acknowledged the strain on the state budget.

“Massachusetts is also seeing a migrant crisis like like no other state in the nation, one that has put our emergency family shelter system and our budget at a breaking point at the moment,” Michlewitz told members of the Black Economic Council of Massachusetts. “And although our fiscal outlook is still pretty strong, and we built up our reserves to record highs, the budget before us today that we’re dealing with is going to be one of the most challenging I’ve had to deal with as the chair.”

Healey capped the family shelter system at 7,500 families last fall, and since then close to 800 families have joined a waiting list hoping for a spot in stable shelter. American citizens do not get priority over those who recently entered the country.

While calling for federal aid and reforms to alleviate the crisis, Healey has also attempted to help families in shelters to obtain work permits so they can become self-sufficient and help employers fill holes in the labor force.

In order to get a spot in the Emergency Assistance system, a noncitizen must have come to the U.S. through legal means, as a refugee, asylum-seeker or through another legal process.

“In Massachusetts, they get a right to shelter, driver’s licenses, in-state tuition. All sorts of things. Gov. Healey should be turning the magnets off, because it’s unsustainable,” Barbaro said.

Citing rising costs, lawmakers in both the House and Senate recently passed bills to put limits on the amount of time a family can stay in the EA shelter system. Both would restrict stays to nine months, with different ideas for exceptions and extensions.

Asked about the idea of cutting shelter costs by placing time limits on family stays, Murray said it was not enough.

“The exceptions to the rule overwhelm the reform, I really think the only thing that we can do right now is to repeal the right to shelter,” he said.