The Federal Emergency Management Agency said it has already dispensed close to $200 million in emergency housing assistance and has put 34,000 people in the New York and New Jersey metropolitan area up in hotels and motels.

But local, state and federal officials have yet to lay out a specific, comprehensive plan for finding them long-term places to live, even as cold weather sets in. And given the scarcity and high cost of housing in the metropolitan area and the lack of open space, it could prove a monumental undertaking.

For example, can enough vacant apartments be found? Will the task involve huge, Hurricane Katrina-style encampments of trailer homes? And if so, where will authorities put the trailers? In stadiums? Parks?

Authorities cannot answers those questions yet.

“It’s not going to be a simple task. It’s going to be one of the most complicated and long-term recovery efforts in U.S. history,” said Mark Merritt, president of Witt Associates, a Washington crisis management consulting firm founded by former FEMA director James Lee Witt.

Tactics that FEMA used in other disasters could be difficult to apply in the city. For example, Merritt said, it’s impossible to set up trailers in people’s driveways if everyone lives in an apartment building, and it’s harder to find space to set up mobile homes.

Sandy killed more 100 people in 10 states but vented the worst of its fury on New Jersey and New York. A week after the storm slammed the mid-Atlantic and the Northeast, 1.4 million homes and businesses remained in the dark.

Another storm — a nor’easter packing heavy rain and gusts of 50 to 60 mph — was headed for the metropolitan area Wednesday, threatening more flooding and power outages that could undo some of the repairs made in the past few days.

With the temperatures dropping into the 30s overnight, people in dark, unheated homes were urged to go to overnight shelters or daytime warming centers.

Because so many voters have been displaced by the storm, New York Gov. Andrew Cuomo issued an executive order allowing people to vote in Tuesday’s statewide and presidential elections at any polling place in the state. New Jersey had already taken similar measures.

“Just because you are displaced doesn’t mean you are disenfranchised,” Cuomo said. “Compared to what we have had to deal with in the past week, this will be a walk in the park when it comes to voting.”

As for long-term housing for the homeless, Homeland Security Secretary Janet Napolitano said Monday that the government is looking into using everything from hotels and motels to FEMA trailers and prefab homes.

“Given the extent of need, no option is off the table,” she said. “All of them will have some place in this puzzle.”

Napolitano said the government’s first priority is getting people to a warm place where they can eat a hot meal. Beyond that, the government wants to find housing as close to people’s homes as possible.

“Whether we’ll be able to accomplish that, I couldn’t say,” she said. “We’re just now getting a handle on housing.”

Officials have yet to even establish the magnitude of the problem.

In New York City, Mayor Michael Bloomberg said Monday that officials are going door-to-door in hard-hit areas to assess the need for shelter. He said the worst-case estimate is 40,000 people, half of them in public housing.

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.