As the state nears its threshold level for housing homeless families, the Healey administration on Tuesday announced a new $5-million program to help community groups provide short-term housing.

The federal funding, distributed by the social services nonprofit United Way of Massachusetts Bay, will go to local organizations to create short-term overnight sites for “families and pregnant individuals with no alternative shelter options,” according to Healey’s press office.

Gen. L. Scott Rice, the state’s emergency assistance director, said Massachusetts anticipates hitting the 7,500-household threshold for families enrolled in the emergency shelter system on Wednesday or Thursday. As of Tuesday, there were 7,439 families enrolled in emergency shelter statewide.

“Massachusetts is in a new phase of managing our emergency shelter system,” Rice said in a press conference at the State House Tuesday. “We are doing everything possible to ensure the safety and wellbeing of families.”

The United Way will run an application process for community groups to obtain funds that could be used for safety net shelter facilities. Bob Giannino, chief executive of the United Way of Massachusetts Bay, said he doesn’t yet know how many families may be helped.

“Our hope is that it would get us closer to thousands [of families],” he said, “but we’re literally days into crafting this work.”

On Tuesday, Rice also announced that the state will activate an additional 75 National Guard members to join 300 already providing help at existing emergency shelters. The guardsmen will be assisting in upcoming work authorization and employee clinics run with the Department of Homeland Security this month.

Rice said nearly 300 people in the shelter system have already enrolled in MassHire, a state program meant to connect job seekers with local businesses. The organization has connected immigrants with work authorization with employers like Dunkin’, Market Basket, Walmart, Yankee Candle and Cooley Dickinson Hospital, he said.

The announcement of new funding came hours after the House released a supplemental spending bill that included $250 million requested by Gov. Maura Healey for the emergency shelter system.

But the money comes with a catch. The bill sets aside $50 million for the state to create overflow shelters for the first 30 days after shelter capacity is reached — or requires the state to lift the 7,500-family cap. The Healey administration is now reviewing the bill.

Massachusetts is the only state in the nation with a right-to-shelter law, a 1983 rule that legally requires the state to shelter unhoused families with children. While the Healey administration has said it is not ending the law, it has also said it won’t be able to fulfill its obligations when the system reaches the threshold. The 7,500 household figure is not in the law.

Under new rules unveiled last week, the Healey administration will implement a waitlist and be triaging families into four tiers using a health questionnaire. The first is women facing high-risk pregnancy, families with a member who has a tracheotomy or an infant, and families at risk for domestic violence.

The second is for families with children between three to six months, a family member in the third trimester of pregnancy, family member with three or more chronic conditions, those who use refrigerated insulin, and those with medical devices. The third tier is for families with children six to nine months, family with a primary caregiver who is 70 years old or over, and those with other medications requiring refrigeration. Other families will be deemed “priority four.”

Following the announcement from the Legislature, advocacy group Lawyers for Civil Rights said it anticipates dismissing its lawsuit against the Healey administration over the shelter cap in the coming days.

"Lawyers for Civil Rights applauds the Legislature’s announcement today that it will appropriate $250 million to help alleviate the humanitarian crisis facing the Commonwealth’s emergency shelter system. We are proud that the lawsuit we filed late last month helped bring about this result," said Iván Espinoza-Madrigal, executive director of the organization.