Story highlights Obama says he'll sign the storm relief bill "as soon as it hits my desk"

The Senate approves a $50 billion relief package for Superstorm Sandy victims

Senators voted down a call to offset that spending with other cuts

The House's failure to vote on relief in December outraged politicians from both parties

The Senate approved more than $50 billion in aid to states battered by Superstorm Sandy on Monday, four weeks after a delay that sparked bipartisan fury from Northeastern lawmakers.

The money includes grant funding for owners of homes and businesses, as well as funding for public improvement projects on the electrical grid, hospitals and transit systems to prevent damage from future storms. In a statement from the White House, President Barack Obama said he would sign the measure "as soon as it hits my desk."

The 62-36 vote came after senators turned back an attempt to require budget cuts elsewhere to offset the cost of storm relief, a proposal that further irked several members.

"For decades, taxpayers from New York have sent their money when disasters occurred, with fires on the West Coast or floods in the Missouri and Mississippi valleys or hurricanes in Louisiana and Florida," said Sen. Chuck Schumer, D-New York. "We've sent our tax dollars, billions of them -- and now, all of a sudden, some are suggesting we should change the rules when we are hit by the first major disaster to hit the New York City region in a very long time. That's not fair. That's not right."

Sandy killed at least 113 people in the United States, flooded much of lower Manhattan and Long Island and smashed New Jersey seaside towns when it struck October 29. Tens of thousands of families are still displaced or lack adequate heat to deal with the winter cold that included an Arctic blast last week.

Nicola Chati, a resident of New York's Staten Island, said living in temporary housing has been "really hard on the kids."

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"They don't know when they're going home," Chati, whose family awaits a decision on whether their home will be repaired or condemned, told CNN over the weekend. "That's all they want."

New York has estimated its storm-related costs at nearly $42 billion, while New Jersey's estimated losses totaled about $37 billion. In a joint statement, New York Gov. Andrew Cuomo, New Jersey Gov. Chris Christie and Connecticut Gov. Dannel Malloy praised the Senate for approving the funds "despite the difficult path in getting to this moment."

"To all Americans, we are grateful for their willingness to come to our aid as we take on the monumental task of rebuilding, and we pledge to do the same should our fellow citizens find themselves facing unexpected and harsh devastation," they said.

Before approving the relief bill, senators voted 62-35 to reject an amendment by Sen. Mike Lee, R-Utah, that would have required Congress to pay for storm relief with other cuts.

"My heart goes out" to residents of the stricken area, said Lee, a tea party favorite elected in 2010. But he added, "We have to stop and consider the fact that we are more than $16 trillion in debt and that we're adding to that debt at a rate of more than $1 trillion every year."

But Sen. Robert Menendez, D-New Jersey, noted that in 2005, it took Congress just 11 days to approve $60 billion in aid for the Gulf Coast after Hurricane Katrina, while Monday marked 91 days since Sandy hit.

"I personally am tired of listening to the voices of patience and delay and suggesting that somehow we as citizens of the United States are second-class citizens, waiting for this government to respond to the needs of fellow Americans."

The Senate approved a $60 billion aid package for the hard-hit region in late December. But House Speaker John Boehner scrapped a vote on the bill before the clock ran out on the last Congress on January 1, leading to howls of outrage from New York and New Jersey officials. Christie, the keynote speaker at last year's GOP convention, said the move explained "why the American people hate Congress."

Chastened House leaders quickly scheduled new votes, passing $9 billion to bolster the federal flood insurance program in the first week of January and voting 241-180 to approve another $50 billion on January 15.

The Senate also passed the flood insurance bill, which Obama signed in early January. After Monday's vote, Obama said that for people struggling to rebuild, "every day without relief is one day too many."

"So while I had hoped Congress would provide this aid sooner, I applaud the lawmakers from both parties who helped shepherd this important package though," he said.