In 2021, New York’s shelter system was under strain, with 61,000 residents. Officials said it was at capacity — or over.

In 2023, the system is on track to house twice as many people.

The population reached an eye-popping record 100,000 this week, thanks to familiar factors — the pandemic, skyrocketing rents — and acute ones: economic turmoil abroad and politicians in America seeking to thrust New York into a border crisis thousands of miles away.

The rush of arrivals from the south has had people living not just in traditional shelters, but in temporary accommodations in hotels, tents and even gymnasiums. The Roosevelt Hotel, which opened in Midtown in 1924 to fanfare and where annual New Year’s Eve radio broadcasts popularized “Auld Lang Syne,” will in coming months turn over all 1,000 of its rooms to migrants.

Officials described this week as a “tipping point” — for the first time, migrants composed the majority of those in shelters. The startling new number of shelter residents is further troubling because of the numbers it isn’t reflecting.

“It’s scary that we are at this benchmark and we don’t even know how accurate it is, how many are unaccounted for,” said Adolfo Abreu, the housing campaigns director at Vocal-NY, a social services agency.

Such an explosion of migrants, which is estimated to cost $4.3 billion by July 2024, would test any American city. In New York, the arrivals were met by a system that had already been under pressure because of factors of the city’s own making.

New Yorkers spend more on rent than ever. And when they stop being able to pay, lose their homes and avail themselves of the city’s unique right to shelter, they find it harder than ever to get affordable permanent housing. So they linger longer in the facilities than past generations did — the average stay for families with children is more than 530 days, according to the most recent figures, double 15 years ago.

More homeless people compete for homes, until the shelter becomes the home.

In 2022, the floodgates opened when a bus arrived from Texas carrying a mere 40-some people. It was met by aid workers with blankets and the handshakes and cheers of a city that prided itself on stepping up.

The applause stopped, and the cameras turned elsewhere, but the buses — and airplanes — kept coming. Shelters opened faster than pop-up restaurants, more than 170 since last spring, sometimes overnight.

“There’s not a day I go to bed and where I’m not like ‘Do we have enough for tonight?’” said Anne Williams-Isom, the deputy mayor for health and human services.

Where are those 100,000 people living? What does that life look like?

Renee Culp, 50, has stayed in shelters for a decade. “It’s been hell,” she said. “You have no resources.” Try finding a job with no computer to look for one, she said.

A more recent arrival is Elliot Ramirez, 36, a Colombian carpenter who left his family and traveled through Nicaragua and Mexico to swim the Rio Grande to Texas. He said a “foundation” gave him a free plane ticket and for two months he has stayed at the Bedford-Atlantic Armory shelter in Brooklyn.

It’s been a whirlwind. The food is OK. The place is uncomfortably crowded, though so many inside speak Spanish that it reminds him of home. Jobs are hard to find without a work visa, so he can’t use the skills he brought with him.

“It’s more complicated in New York,” he said.

Roger Davis, 65, entered a shelter in the Bronx after an outreach worker found him sleeping in a subway car. He lived indoors for a year until it got too crowded. Nobody seemed to follow the rules anymore, smoking anywhere they pleased. The bathrooms became filthy, and staff members, exhausted, scolded anyone in front of them.

Mr. Davis returned to the streets. Sometimes he sleeps in the subways, sometimes on the sidewalks, in shanties made from shipping pallets.

“It’s easier that way,” he said.

Ezekiel Lee, 57, at a shelter on 12th Street in Brooklyn, said there is more waste in the system — razors used once and thrown away, leading to a shortage.

He said the arrival of migrants in such numbers — “and don’t get me wrong, I’m sympathetic” — is straining the system. “It’s not one thing,” he said. “It’s many different things.”

Put another way: “This is a humanitarian crisis,” said Christine Quinn, the former speaker of the New York City Council, who now heads the shelter agency Women In Need. “If there’s a goddamn roadblock, get over it.”

Mr. Abreu, with Vocal-NY, said the population of 100,000 is unlikely to shrink soon.

“A lot of us are one income shock away from being homeless,” he said. “That’s a very precarious situation that, if we don’t dig in, the 100,000 could double or triple.”

Nate Schweber and Olivia Bensimon contributed reporting.