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.