Cuomo, a Democrat, put the damage from the late October storm at $40 billion to $50 billion for New York alone, with the total likely to rise.
"We need help. These are big numbers, even for New York," he told a news conference while flanked by members of the state's congressional delegation.
After meeting White House aides, House of Representatives Speaker John Boehner and other congressional leaders, Cuomo said Boehner wanted a supplemental spending bill on Sandy costs passed by the end of the year.
Congressional aides said there has been no clear consensus on its size. But they said it would likely be far less than the nearly $80 billion New York and New Jersey, the states most heavily hit by Sandy, are seeking combined.
Christie is asking the federal government to reimburse the state for 100 percent of emergency costs for at least 90 days after Sandy swept ashore on Oct. 29.
Cuomo said he and Boehner did not discuss whether reconstruction costs would be offset by spending cuts elsewhere. Offsets are a key issue given the budget crisis involving deep spending cuts and tax hikes due to take effect in January.
As of Thursday, FEMA's disaster relief fund had about $5.06 billion in funds left after making Sandy obligations totaling $2.2 billion, according to FEMA reports.
Congress has budget authority to add about another $5 billion to the fund, but would have to vote to approve the request.