The vote was 241-180, and officials said the Senate was likely to accept the measure early next week and send it to President Barack Obama for his signature. Democrats supported the aid in large numbers, while majority Republicans opposed it by a lopsided margin.
"We are not crying wolf here," said Rep. Chris Smith, R-N.J., one of a group of Northeastern lawmakers from both parties who sought House passage of legislation roughly in line with what the Obama administration and governors of the affected states have sought.
Democrats were more politically pointed as they brushed back Southern conservatives who sought either to reduce the measure or offset part of its cost through spending cuts elsewhere in the budget.
"I just plead with my colleagues not to have a double standard," said Rep. Carolyn Maloney of New York. "Not to vote tornado relief to Alabama, to Louisiana, to Mississippi, Missouri, to - with Ike, Gustav, Katrina, Rita - but when it comes to the Northeast, with the second worst storm in the history of our country, to delay, delay, delay."
One key vote came on an attempt by Rep. Rodney Freylinghuysen to add $33.7 billion to an original allotment of $17 billion in aid. That roll call was 228-192 and Democrats broke 190-2 in favor, while Republicans opposed it overwhelmingly, 190-38.
Similarly, on final passage, 192 Democrats joined 49 Republicans in support. Opposed were 179 Republicans and one Democrat.
Earlier, conservatives failed in an attempt to offset a part of the bill's cost with across-the-board federal budget cuts. The vote was 258-162.
Rep. Mark Mulvaney, R-S.C., arguing for the reduction, said he wasn't trying to torpedo the aid package, only to pay for it. "Are there no savings, are there no reductions we can put in place this year so these folks can get their money?" he asked plaintively.
Critics said the proposed cuts would crimp Pentagon spending as well as domestic accounts and said the aid should be approved without reductions elsewhere. "There are times when a disaster simply goes beyond our ability to budget. Hurricane Sandy is one of those times," said Rep. Hal Rogers of Kentucky, chairman of the House Appropriations Committee.
Sandy roared through several states in late October and has been blamed for 140 deaths and billions of dollars in residential and business property damage, much of it in New York, New Jersey and Connecticut. It led to power outages and interruptions to public transportation that made life miserable for millions, and the clamor for federal relief began almost immediately.
The emerging House measure includes about $16 billion to repair transit systems in New York and New Jersey and a similar amount for housing and other needs in the affected area. An additional $5.4 billion would go to the Federal Emergency and Management Agency for disaster relief, and $2 billion is ticketed for restoration of highways damaged or destroyed in the storm.
The governors of the three states most directly affected praised the congressional action.
"We are grateful to those members of Congress who today pulled together in a unified, bipartisan coalition to assist millions of their fellow Americans in New York, New Jersey, and Connecticut at their greatest time of need," said a joint statement issued by New York Governor Andrew M. Cuomo, New Jersey Governor Chris Christie and Connecticut Governor Dannel P. Malloy. "The tradition of Congress being there and providing support for Americans during times of crisis, no matter where they live across this great country, lives on in today's vote in the House of Representatives."
The governors said they "anticipate smooth passage when this package moves back to the Senate for final approval and for this long-awaited relief to finally make its way to our residents."
The Senate approved a $60 billion measure in the final days of the Congress that expired on Jan. 3, and a House vote had been expected quickly.
It is highly unusual for a majority party to bring legislation to a vote that its own rank-and-file opposes, but in this case, Speaker John Boehner, R-Ohio, and the leadership had little or no choice.
Boehner unexpectedly postponed the vote in the final hours of the expiring Congress as he struggled to calm conservatives unhappy that the House had just approved a separate measure raising tax rates on the wealthy.
The delay drew a torrent of criticism, much of it from other Republicans.
"There's only one group to blame for the continued suffering of these innocent victims, the House majority and their speaker, John Boehner," New Jersey Gov. Chris Christie said on the day after the delay was announced. Rep. Pete King of New York added that campaign donors in the Northeast who give to Republicans "should have their head examined."
Less than two weeks later, the leadership brought legislation to the floor under ground rules designed to satisfy as many Republicans as possible while retaining support from Democrats eager to approve as much in disaster aid as possible.
Across the capitol, majority Democrats indicated they would probably not seek changes.
"While the House bill is not quite as good as the Senate bill, it is certainly close enough," Sen. Charles Schumer of New York said. "We will be urging the Senate to speedily pass the House bill and send it to the president's desk."
Congress has already approved a $9.7 billion increase in a fund to pay federal flood insurance claims, much of it expected to benefit victims of Sandy.
The political veered into the personal at times during hours of debate.
In remarks on the House floor, Rep. Bill Pascrell, D-N.J., said one South Carolina lawmaker who has criticized the measure "personally took a small business" disaster loan in the past. While he didn't mention any names, South Carolina Rep. Mulvaney has said he received such a loan.
Mulvaney later told reporters the comparison was a poor one. He said that unlike funds in the Sandy legislation, the loan he received was approved within the budget, and not as an add-on that increased the deficit.
In the weeks since the storm hit, the Federal Emergency Management Agency has spent about $3.1 billion for construction of shelters, restoration of power and other immediate needs after the late-October storm pounded the Atlantic Coast with hurricane-force winds and coastal flooding.
Officials say Sandy is the most costly natural disaster since Hurricane Katrina in 2005. The storm damaged or destroyed 305,000 housing units in New York, and more than 265,000 businesses were disrupted there, officials have said. In New Jersey, more than 346,000 households were destroyed or damaged, and more than 40,000 families remain living out of their homes, according to officials.