The US House of Representatives has passed a measure to increase the country's debt ceiling by a vote of 269 to 161 and sent it to the Senate for final congressional approval.
The Senate is expected to vote on Tuesday -- the day that the Treasury Department has said it will not be able to borrow more funds to pay all of the nation's bills.
The compromise move would cut about $2.4tn from the deficit over the next 10 years.
Financial markets worldwide have been rattled by uncertainty over whether the compromise plan could pass the House in the face of objections from conservative Tea Party Republicans and from liberal Democrats.
Having a deal in place by Tuesday to raise the US government's $14.3 trillion borrowing limit will remove the risk of the United States not being able to borrow money to pay all of its bills.
A debt default by the world's largest economy would send shockwaves through the international economic system.
In the hours leading up to the House vote, Republican and Democratic leaders worked furiously to sell their rank-and-file on a deal reached with President Barack Obama in a bid to end an acrimonious impasse that has undermined Americans' faith in their political institutions and hurt America's image abroad.
But fears remained that the US could still be hit by a damaging credit ratings downgrade, which would raise US borrowing costs, threatening a fragile economic recovery and rattling global investors.
The compromise plan calls for spending cuts over 10 years but no new taxes, creates a powerful new congressional committee to recommend a deficit-reduction package by late November and raises the US borrowing limit into 2013.