Homeless families seeking shelter in D.C. could face tougher screening under new regulations proposed by Mayor Muriel Bowser.

The mayor is pushing a bill expanding the paperwork requirements for the homeless, who would have to prove they aren’t traveling to D.C. just to take advantage of the city’s shelter system. It would also make it easier for social workers to disqualify applicants they suspect have other housing options.

Bowser asked D.C. Council members at a meeting Tuesday to act on her proposal by the end of this year, warning of overflowing shelters as the days grow colder. She said the measure — first filed in September, and facing stiff opposition from some council members and homeless advocates — is needed to prevent the misuse of services by those who live outside the District.

“We have an obligation to serve our residents. But we cannot serve the entire region,” Bowser said. At present, she added, “We’re serving everybody else’s residents. We can’t serve our own. Our own residents are standing at the back of the line.”

D.C. Council Chairman Phil Mendelson (D) said Wednesday that he did not plan to move the bill forward before January.

D.C. is dealing with a continuing homeless crisis that escalated in 2010 during the economic downturn and was made worse by a lack of affordable housing and rising real estate prices. Here are nine facts about being homeless in D.C. (Claritza Jimenez/The Washington Post)

The legislative effort marked a shift in tone for Bowser, who denounced the more conservative approach to homelessness taken by her predecessor, former Mayor Vincent C. Gray, and who has made ending chronic homelessness a centerpiece of her agenda.

It also touches on larger legal and philosophical questions about the meaning of a residency requirement for people who have no place to call home.

Bowser administration officials say the law is needed because the city’s shelters are being swamped during the winter, driving up costs and diverting resources that could be better used moving homeless families out of temporary shelter into longer-term housing.

According to the D.C. Department of Human Services, the city is spending $80,000 every night on motel rooms for homeless families. During the winter, the department asserts, about 12 percent of those seeking family shelter are not District residents. It was not immediately clear how DHS arrived at that estimate.

The plan is drawing fire from critics who argue that more time is needed to weigh the mayor’s proposal and that D.C. should not be lowering the gate against families in danger of freezing on the streets.

Amber Harding, an attorney with the Washington Legal Clinic for the Homeless, said the proposed tweaks to eligibility requirements for homeless services are “extremely troubling” and would worsen a system that already throws up too many barriers for families seeking shelter.

“We get calls from families almost every day because they can’t meet the bureaucratic hurdles to prove their homelessness or their D.C. residency,” Harding said.

Council member Robert White (D-At Large) compared the plight of the District’s homeless to that of undocumented immigrants, whom the city seeks to protect through “sanctuary city” policies that limit police officers’ cooperation with federal immigration agents.

“I think homelessness is no different,” White said. “We have an obligation to people even if they happen to sometimes live across the border... I think homelessness doesn’t know jurisdictions.”

The mayor took to Twitter Tuesday evening to “clarify” and defend her position. “District taxpayers should not be put in the position of providing services for the entire region when there is so much need here,” she wrote in one of four Tweets.

D.C. already has a residency requirement for homeless families seeking services, but officials say it is too lax. The new law would require two documents to prove D.C. residency from a list of possible options, some of which may be scarce among the homeless — such as a utility bill or pay stub.

It would also place stricter rules on who is eligible for emergency hospital beds. Officials say some homeless people are staying after their treatment is over, preventing others from getting emergency medical care.

DHS Director Laura Zeilinger said families who don’t qualify for emergency shelter could still qualify for other social services — such as financial assistance to help them stay elsewhere or counseling.

“We’re not trying to put people out on the street,” she said.