NEW YORK — The crowds outside the Roosevelt Hotel in midtown Manhattan this week would have been familiar in any number of U.S. cities struggling to contain a crisis of homelessness: dozens of people languishing on sidewalks, camping out on flattened cardboard boxes day and night.

But for New York City, the scene — made up of migrants waiting for beds in the city’s overburdened shelter system — was unusual. And it raised a difficult question: Will this become a new normal?

New York has avoided the kinds of widespread encampments that are more common in cities on the West Coast, largely because of a unique legal agreement that requires the city to provide a bed for anyone who requests one. No other major city in the United States has a similar mandate, known as a “right to shelter.”

But what happens when a city that is obligated to provide shelter for everyone runs out of shelter?

This week, Mayor Eric Adams declared, in dire terms, that there was no more room left for migrants. His administration was coming up with a plan, Adams said, so that “we don’t have what’s in other municipalities where you have tent cities all over the city,” evoking images of homeless camps in places such as San Francisco and Seattle on the streets of New York.

“We need help,” Adams said. “And it’s not going to get any better.”

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Already, New York is home to thousands of people who are considered “unsheltered,” meaning they sleep on the streets or in the subways instead of opting for a shelter bed. But the vast majority of New York’s homeless population sleeps in shelters — in stark contrast to cities such as Los Angeles. New York’s harsher winters also make large-scale outdoor encampments less feasible than on the West Coast.

“Tent cities are on the rise around the country because of an extreme and growing lack of affordable housing,” said Maria Foscarinis, founder of the National Homelessness Law Center, a nonprofit. “The reason they are not as prevalent in New York is the city’s legal right to shelter.”

That legal requirement should theoretically continue to keep New York’s homeless people sheltered, and city officials say there are other sites available to use, including ones that require federal approval. But the city is now struggling under the weight of nearly 100,000 migrants who have arrived since last year. More than 56,000 migrants still remain in New York City’s shelters. And the pace has not slowed. Last week alone, 2,300 new migrants arrived.

New York City has opened 194 sites to house the newcomers in any usable facilities it could find — including hotel ballrooms, parking lots, former jails and an airport warehouse. The city’s homeless shelter population now exceeds 100,000 people, a record high.

“We are at the desperation stage,” said Mark Levine, the Manhattan borough president, who has joined other city officials in pleading for more federal help. “We’re going to have to make more and more difficult decisions on siting facilities that at this point are all going to disrupt some aspect of life here.”

During a news conference Wednesday, Deputy Mayor Anne Williams-Isom said the city has been a “guardian of the right to shelter,” but the system was buckling under pressure.

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In response to questions about potential sites for sheltering migrants, including Randall’s Island and Central Park, she said all options were on the table. “People on the one hand cannot accuse us of not having enough space,” she said, “and then on the other hand tell us, ‘Well, you can’t go here and you can’t go there.’” Some shelter sites have been delayed because of fierce opposition in neighborhoods where they would be located.

The city’s legal obligation stems from a class-action lawsuit that was filed in the late 1970s, which argued that a right to shelter existed under the New York state Constitution.

To settle the lawsuit, the city reached an agreement in 1981 to provide shelter for every homeless man who applies for it, which has since been expanded to women and families with children. The agreement also laid out the standards for care, including bed size and staff-to-resident ratios.

Despite repeated challenges by mayoral administrations to weaken the mandate, it has endured for four decades because “New Yorkers don’t want to see mass homelessness,” said Joshua Goldfein, a staff attorney at the Legal Aid Society, which worked on the lawsuit that led to the 1981 agreement with the lawyer Robert Hayes, who founded the Coalition for the Homeless.

“They don’t want to see people living in the streets with their children,” he said.

In West Coast cities that have struggled with homeless encampments, the shelter infrastructure is much more limited than in New York, according to Dennis Culhane, a professor of social policy at the University of Pennsylvania.

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In May, the Adams administration asked a New York court to relieve it from some obligations under the right-to-shelter agreement. The court proceeding is still ongoing.

This week, the Legal Aid Society and the Coalition for the Homeless, which monitors conditions in shelters, said that if asylum-seekers continue to be stuck without beds, “we will have no choice but to file litigation to enforce the law.”

For now, New York is taking steps to try to deter migrants from coming, including by distributing flyers at the U.S. southern border telling them that they will not be guaranteed services if they come to the city.

Advocates for migrants and homeless populations have argued that the Adams administration could be doing more to free up shelter space by expanding eligibility for housing vouchers and increasing staff to manage the logistics of helping migrants move on. Some migrants who want to move out of New York are unable to because of delays in securing a driver’s license, lawyers say.

The city has repeatedly urged the Biden administration to provide more aid and to expedite the federal process for migrants to legally work. On Wednesday, the city also announced a partnership with several universities to recruit student volunteers to help migrants fill out asylum applications.

Despite shelter capacity reaching its limits, Donovan Richards, the Queens borough president, said the prospect of tent cities popping up throughout New York is unlikely. There are still more emergency shelters that can be opened, he said, including a new site that can fit 1,000 people and is set to open soon in the parking lot of a psychiatric center in Queens.

“I get a ping on my phone at least twice or three times a week about a new hotel opening up or a new site being proposed,” Richards said. “That’s going to be the norm for a while, but that’s going to prevent people from sleeping on the sidewalk.”

Jeffery C. Mays contributed reporting.