The bill put forward by the White House already passed in the Senate. But the Republican leadership in the House, smarting from battle with Democratic President Barack Obama over "fiscal cliff" budget talks, has stalled.
"With all that New York and New Jersey and our millions of residents and small businesses have suffered and endured, this continued inaction and indifference by the House of Representatives is inexcusable," governors Chris Christie and Andrew Cuomo said in a joint statement.
"It has now been 66 days since Hurricane Sandy hit," they said. "This failure to come to the aid of Americans following a severe and devastating natural disaster is unprecedented.
"The fact that days continue to go by while people suffer, families are out of their homes, and men and women remain jobless and struggling during these harsh winter months is a dereliction of duty. When American citizens are in need we come to their aid. That tradition was abandoned in the House last night."
Flooding from Sandy, which hit the densely populated northeast with hurricane force, damaged tens of thousands of homes and businesses, as well as pummeling critical infrastructure.
Representative Peter King, a Republican from New York, sharply criticized his own party for not expediting a vote on the aid.
"The Republican Party has said it's the party of 'family values.' Last night, it turned its back on the most essential value of all, and that's to provide food, shelter, clothing and relief for people who have been hit by a natural disaster," King told CNN.