High winds and flooding caused extensive damage in the US north-east Reuters

Millions of people across the US mid-Atlantic were today counting the cost of "once-in-a-lifetime" post-tropical cyclone Sandy, after punishing winds and devastating floods brought New York City to a standstill, left around 7.5 million people without power and claimed at least 33 lives.

As the storm – which was reclassified from a hurricane shortly before making landfall on Monday near Atlantic City, New Jersey – continued inland with weakened but still powerful winds, Barack Obama declared a "major disaster" in the New York City area, a move designed to free up federal aid for inhabitants.

Obama held a video-teleconference from the Situation Room at the White House with members of his cabinet and the emergency services to ensure not only that rescue and relief operations are well under way but to speed up efforts to restore power.

A White House statement said: "The president told his team that their top priority is to make sure all available resources are being provided to state and local responders as quickly as possible."

New Jersey governor Chris Christie during a press conference this morning called the level of devastation "unthinkable".

"This is beyond anything I ever thought I would see," he said.

He gave a stark description of the problems facing his state. More than 2 million people are without power, mass transit is at a standstill, roads and bridges closed amid severe damage, 29 hospitals are running on generators or experiencing power issues. About 5,500 people are in shelters and the weather is still so bad that it is difficult to assess the full extent of the damage.

He warned people to stay away from the state's notorious Jersey shore, much of which has been washed away. "The amusement pier at Seaside Park is essentially half washed out. I don't know if it's the rollercoaster or the log flume that is now in the ocean," he said.

In New York, the mayor, Michael Bloomberg, said the death toll in the city from storm had now reached 10. He said it could be three days or more before power is restored to hundreds of thousands of people, and the crippled subway service was unlikely to resume for four or five days.

Earlier, the chairman of the Metropolitan Transportation Authority (MTA), Joseph J Lhota, said Sandy had been the most destructive storm in the subway network's 108-year history.

A dramatic fire that destroyed at least 50 homes in Breezy Point, Queens, was still raging on Tuesday, while an unprecedented seawater surge of nearly 14ft left much of lower Manhattan flooded, including subway stations and the electrical system that powers Wall Street. The previous record had been set by hurricane Donna in 1960, which prompted a surge of 10ft.

"Hitting at high tide, the strongest surge and the strongest winds all hit at the worst possible time," Jeffrey Tongue, meteorologist for the weather service in Brookhaven, New York, told Reuters. "Hopefully it's a once-in-a-lifetime storm."

Winds as high as 90mph and sustained at 80mph were recorded as Sandy made landfall on the New Jersey coast around 8pm EDT. Officials reportedly connected at least 33 deaths to the bad weather throughout the affected region, with fatalities reported chiefly in New York but also in New Jersey, Connecticut, Pennsylvania, Maryland, Massachusetts and West Virginia. Police in Toronto said a woman had been killed by flying debris.

In the Caribbean, which Sandy had pummelled on its way to the US east coast, 69 people were reported to have died, most of them in Haiti.

As Sandy passed west from New Jersey across southern Pennsylvania on Tuesday, the National Hurricane Center said it was still reaching sustained winds of 65mph. The storm is expected to take a northwards path towards Canada later on Tuesday and heavy snowfall, alongside high winds, are expected in some states. Chicago officials warned residents to stay away from the shore of Lake Michigan amid fears of winds of up to 60mph and waves of more than 24ft. According to the American Red Cross, nearly 11,000 people spent the night in 258 shelters across 16 states.

Floodwaters from hurricane Sandy rush down an elevator shaft into Hoboken PATH station. Photograph: Reuters/Port Authority Trans-Hudson

In New York, where nearly 2 million people were still without power at 8am on Tuesday morning, a major cleanup operation will be necessary to get the city back on its feet. The stock exchange remained closed for the second day running.

In a statement, the MTA said it could take between 14 hours and four days to get floodwater out of subway tunnels. "We are assessing the extent of the damage and beginning the process of recovery," Lhota said. "In 108 years our employees have never faced a challenge like the one that confronts us now."

One of the most worrying events of Monday night was the emergency evacuation of 200 patients from New York University's Tisch hospital after the institution's backup generator failed. NYU's medical dean Robert Grossman told the Associated Press that among the people moved were 20 babies from the neonatal intensive care unit who were on battery-powered respirators and who had to be carried to ambulances waiting to take them to other hospitals.

Sandy caused a levee to break in northern New Jersey on Tuesday, flooding the towns of Moonachie, Little Ferry and Carlstadt with up to 5ft of water.

Officials told Reuters there were no reports yet of fatalities.

Writing on Twitter, Chris Christie said the cost of the storm was incalculable. "The devastation on the Jersey shore is some of the worst we've ever seen," he said. "The surge was so strong we have rail cars on the Jersey Turnpike this morning. New Jersey is a tough place … We will dig out from under and we will be back."