But he said as many as 20,000 will probably get their heat and power back within a few days. Ultimately, the number of people who need housing could be under 10,000, he said.
In New Jersey, state officials said they are still trying to figure out how many people will need long-term housing. At least 4,000 residents were in New Jersey shelters.
In the meantime, Bloomberg appointed Brad Gair, an emergency management specialist, as chief of housing recovery operations, with responsibility for overseeing the city's efforts to find shelter for those left homeless by the storm.
At a news conference, the mayor asked for patience after reporters pressed Gair for more specifics on how he intended to deal with the problem. Bloomberg pointed out that Gair had been on the job for only four hours.
"I want to assure everyone that every New Yorker who needs a warm place to live and a roof over his or her head is going to have one," Bloomberg said.
Cuomo said that, statewide, solving a problem that extends from city to suburb is "going to be a community-by-community option." While some local governments may want trailers, for instance, others may look to motels or apartment rentals.
In the New York City borough of Staten Island, blue-jacketed FEMA volunteers knocked on doors in a devastated neighborhood, making sure everyone was registered to apply for aid.
Amin and Rachael Alhadad and their four children have been sleeping sitting up in their Jeep. They were supposed to finally meet with FEMA workers on Monday afternoon.
"We're homeless right now and it just keeps getting worse every day," Amin Alhadad said. "We can't shower, we can't use the bathroom, we can't sleep properly. We're struggling right now. I'm losing my job right now due to this."
Alhadad said FEMA told him the government would deposit $2,900 in his account for a hotel, but it has yet to show up. He planned to make some phone calls to see if there were any hotel rooms available. His kids do not want to go to a shelter.
"I'm all out of ideas. I'm dazed and confused," he said.
Relief agencies have been conferring with real estate agents in hard-hit areas like Belle Harbor in the Rockaways section of New York City but have found only a few vacancies, said Yisroel Schulman, president of the New York City Legal Assistance Group. And even if people can find apartments, FEMA payments for temporary housing may fall short in a city known for its expensive housing.
"In the short term, the government is completely ill-prepared," Schulman said.
It's unclear what plans the city, state and federal government had before the storm to deal with a housing crisis of this magnitude. But in 2007, the city Office of Emergency Management held a design competition for post-disaster housing if a Category 3 hurricane smashed the city and left hundreds of thousands homeless.
The winning ideas included building a six-story complex mounted on ship hulls; using debris to create provisional housing; and turning shipping containers into living quarters.
Contributing to this report were Michael Hill, Larry Neumeister, Cara Anna and Christina Rexrode in New York, Alicia Caldwell in Washington and Frank Eltman in Long Beach, N.Y.
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