The call for special aid immediately thrust the storm recovery into the national spotlight, raising questions about the political implications of a major appropriation for New York.
Obama and Congress would need to approve special legislation to provide the funding, even as they are negotiating to avoid the automatic activation of billions in tax increases and spending cuts scheduled to take effect in January -- the so-called "fiscal cliff" that economists fear could plunge the country back into recession.
Undaunted, Cuomo said the White House and Congress had approved special appropriations in the past to help other regions hit by disaster and shouldn't make an exception for Sandy.
"My firm position is that New York needs a supplemental appropriation from the federal government to help us rebuild," Cuomo said in a news conference in Manhattan. "Hurricane Katrina is obviously probably the most popular and noted one. This is quite common, and it has been done in areas that were not nearly as affected as New York."
New York State will not act alone in seeking funding, Cuomo said. He endorsed a regional approach that might include Connecticut, New Jersey and other states affected by the storm, he said. The governor has said Sandy caused a total of around $50 billion in damage to the metropolitan area.
"This is an economy that is important not just to the state," Cuomo said. "This is an economy that is important for the country. The sooner we get the New York economy running, the better for this state and this nation."
Cuomo didn't give a full breakdown of the costs, but earlier in the day his staff confirmed reports that they include $3.5 billion in bridge, tunnel, subway and train repairs; $1.65 billion to rebuild housing destroyed in the storm; and $1 billion for local governments that rang up storm-related costs, such as overtime for first responders.
The governor also is asking for billions in federal funding for businesses struggling to remain afloat as they rebuild. New York State lost a total of $13 billion in commercial activity because of Hurricane Sandy, state officials said.
At his news conference, Cuomo said the special funding would help move money more quickly to small businesses now struggling to deal with the federal Small Business Administration, an agency that is offering loans at 4 percent interest.
"The small business need is going to be profound," he said. "These businesses don't want a small business loan. They don't want to take on more debt. They need someone who can help them open the door of their business. They need a grant program, frankly."
The governor said New York's congressional delegation would work hard to pass the special legislation.
But just hours after news of Cuomo's request hit the Internet, the state's senior senator, Democrat Charles Schumer, cast doubt on the governor's estimate of the damage, saying local governments and residents are still tabulating the toll of the devastation.
"We don't know the amount of damage yet," said Schumer, speaking on Monday in Piermont during a tour of businesses in the Rockland County village's ravaged downtown. "We have to know what the damage is. We want to make a request that is accurate, will be well-received and that covers our needs, and that's what we're doing now."
Still, Schumer said he would work tirelessly to win approval of the governor's request.
"We're going to work hard to get every nickel we can for New York," he said.
Cuomo's request for $30 billion dwarfs the millions, or even billions, of dollars the Federal Emergency Management Agency might give local governments and residents in the coming months. The total budget for the Federal Emergency Management Agency for this year amounts to only about $13 billion.
Cuomo already has asked FEMA to pay 100 percent of the costs that the agency is responsible for covering. FEMA customarily pays 75 percent of disaster-related costs.
Sandy caused horrific destruction on Long Island and in New York City and New Jersey. But Westchester and Rockland counties suffered substantial damage as well and were declared disaster areas. Thousands of residents in the two river counties were still without power on Sunday.
It's not yet clear how much money county residents and businesses lost in the storm.
Westchester County Executive Rob Astorino has said county government suffered at least $100 million worth of damage from Sandy. The storm inflicted about $12 million in damage on Rye Playland, the county-owned amusement park, destroying its boardwalk and felling trees around the property, Astorino said.
Rockland County is still tabulating damage costs, but Sandy decimated the county's Hudson River shoreline, destroying homes, marinas and other structures along the water.
With Christian Wade