Democrats were also outraged.
"It is truly heartless that the House will not even allow the Sandy bill to come to the floor for a vote, and Speaker Boehner should reconsider his ill advised decision," Sen. Chuck Schumer, D- N.Y., said in a statement.
October's storm was the worst natural disaster ever to hit the region, causing billions in damage and leaving 120 people dead.
More than 130,000 people are expected to make claims to the federal government, but without a funding increase only about 12,000 people can be covered with existing funds.
"It doesn't make sense they wouldn't vote on this. There are truly people in need," said Steve Greenberg, whose home was flooded and damaged by fire in the hard-hit Breezy Point section of Queens. "Not of these people are fit to serve," he said.
Grimm said Boehner's decision fuels a perception that the Republican Party does not care about people.
"It buys into the ideology that Republicans don't care and are callous," he said. Grimm said there were enough votes to get the bill passed and that it makes fiscal sense, because the money would go to help spur small businesses.