But the $6 billion battle will be largely fought in the Senate.
The House voted 326 to 90 Tuesday to reverse a controversial $6 billion cut in veterans' benefits included in last year's budget deal.
The House bill would offset the cost of the legislation by extending the budget sequester for mandatory spending cuts by an additional year.
The chamber is almost unanimous in its desire to reverse the cuts, but some Democrats voted against the bill because it would fund the veterans benefits, in part, through further cuts to mandatory domestic spending for social programs they favor.
Democrats on Monday had indicated to Republican leadership that they would not be able to deliver sufficient votes to pass the benefits bill if it was tied to the debt ceiling. The objections to the debt ceiling plan stemmed not from objections to restoring the benefits, but rather from Democrats' concern that they would set a precedent whereby Republicans could tie provisions—even legislation with broad bipartisan support—to a future debt ceiling increase.
In the end, 120 Democrats suppored the veterans measure Tuesday, while 71 voted against it.
The bill now heads to the Senate where it faces an uncertain future. Senate Democrats are arguing that veterans already paid their debt to society and that the legislation to reverse the cost of living adjustment cuts should pass without offsetting the legislation. And Senate Majority Leader Harry Reid, D-Nev., told reporters Tuesday that he would not support the House's sequester extension.
But Senate Republicans are still insisting that legislation to reverse in cuts contains provisions to prevent it from increasing the deficit.
A bill to reverse the vets COLA cuts from Arkansas Democrat Mark Pryor is pending in the Senate. Democrats say they hope to complete that bill this week, but the chamber might adjourn for its President's Day recess as soon as Wednesday because of an expected snow storm.
Sarah Mimms contributed to this article.