By Alison Kuznitz

House Democrats on Friday defeated a Republican bid to restrict migrants’ access to the state’s overflowing emergency family shelter system, a day after the Legislature shipped a supplemental budget to Gov. Maura Healey that would impose a new nine-month limit on shelter stays.

With House Speaker Ron Mariano at the rostrum, lawmakers rejected amendments from Rep. Paul Frost that aimed to install a three-month residency requirement for family shelter and to prioritize Massachusetts residents on the shelter waitlist. Lawmakers rejected Amendment 1393, emergency housing assistance requirements, on a 30-127 roll call vote, and they rejected Amendment 1394, prioritizing Massachusetts residents on the waitlist for emergency housing assistance, on a 27-131 roll call vote.

“I ask that the members consider this amendment so that a family that does need to get emergency shelter can get it, which would not have been a problem a year or so ago, especially those who’ve been here for a long period of time,” Frost, an Auburn Republican, said. “We should give priority to those who have been here longer and longtime residents of Massachusetts, versus a family that just arrived and has been here for an hour. And I think that’s a fair and reasonable thing to do.”

Assistant Majority Leader Alice Peisch argued Frost’s proposals could result in court challenges.

“I would also just like to underscore, as I did a moment ago, that no families — whether they are longtime Massachusetts residents or families that are new to the state — are being put out on the street,” Peisch said. “We do have these overflow shelters. I don’t want anyone to be operating under the assumption that we have Massachusetts residents who are being left out on the street, so once again, I ask you please for the fourth time to reject the residency requirement.”

Anti-homelessness advocates have said that families on the shelter waitlist continue to sleep at Logan Airport, an outcome that lawmakers have tried to avoid as they have injected more and more money into the system and supported new overflow sites.

Democrats also thwarted an amendment from House Minority Leader Bradley Jones to prioritize shelter access for homeless veterans. Amendment 698, homeless veterans prioritization for shelter assistance, was rejected on a 27-129 roll call vote.

Rep. Gerard Cassidy, co-chair of the Joint Committee on Veterans and Federal Affairs, previewed a veterans bill being readied for May that will address programs and benefits extensions.

“This is not a veterans’ bill. This is basically a political ploy to bring the veterans in,” Cassidy said of Jones’ proposal. “This bill that will be coming out is more in tune to what we’re doing.”

As the third day of budget deliberations unfolded, the House unanimously adopted Consolidated Amendment F on a roll call vote, which added more than $8.2 million in housing and energy and environmental affairs investments. The consolidated amendment also removed from the budget proposal a $175 million withdrawal from the Transitional Escrow Fund to be put towards the shelter crisis in fiscal 2025. Legislative Democrats instead authorized that withdrawal in the supplemental budget they passed Thursday.

The amendment includes a bevy of local spending items, including $250,000 to help the City of Quincy manage ferry service at Squantum Point Park, $50,000 for a statue of Sarah Bradlee Fulton in Medford, $62,000 for kitchen equipment at Sudbury’s emergency shelter, and $50,000 to grow the tree canopy in East Boston. Some of the policy provisions impose fines on people who intentionally release helium balloons and establish a deer population control commission.