WASHINGTON — More than 10 weeks after Hurricane Sandy brutalized parts of the heavily populated Northeast, the House approved $50.5 billion in emergency relief for the victims Tuesday night as Republican leaders struggled to close out an episode that exposed painful party divisions inside Congress and out.
The vote was 241-180, and officials said the Senate was likely to accept the measure early next week and send it to President Obama for his signature. Democrats supported the aid in large numbers, but there was substantial Republican backing, too, in the GOP-controlled House.
‘‘We are not crying wolf here,’’ said Representative Chris Smith, Republican of New Jersey and 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 Representative 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.’’
All nine members of the Massachusetts delegation voted for the overall measure.
One key vote came on an attempt by Representative Rodney Freylinghuysen, Republican of New Jersey, to add $33.7 billion to an original allotment of $17 billion in aid. That vote was 228-192 and included heavy Democratic support.
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.
Representative Mark Mulvaney, Republican of South Carolina, argued for the reduction, saying 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.
Critics said the proposed cuts would crimp Pentagon and 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 Representative Hal Rogers of Kentucky, chairman of the House Appropriations Committee.
Sandy roared through several states in October and has been blamed for 140 deaths and billions of dollars in damage, much of it in New York, New Jersey, and Connecticut.
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 Senate approved a $60 billion measure in the final days of the Congress that expired on Jan. 3.
But House Speaker John 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, including Representative Peter King of New York.
Two weeks later, the leadership brought legislation to the floor under ground rules designed to satisfy as many Republicans as possible while retaining Democratic support.
Congress 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.