The measure would suspend the $16.4 trillion limit on federal borrowing through May 18, allowing about $450 billion in new debt to be added to the federal ledger, according to an estimate by the Bipartisan Policy Center.
The Republican-controlled House passed the legislation last week. A successful Senate vote would send the measure to President Barack Obama, who is expected to sign it into law immediately.
Without the bill, the government would default on its obligations by as early as mid-February.
The short-term increase in the borrowing cap is the brainchild of House Republicans, who wanted to re-sequence a series of upcoming budget battles, taking the threat of a potentially devastating government default off the table and instead setting up a clash in March over automatic across-the-board spending cuts set to strike the Pentagon and many domestic programs.
Those cuts — postponed by the recent "fiscal cliff" deal — are the punishment for the failure of a 2011 deficit supercommittee to reach an agreement. The panel was itself established by the hard-fought 2011 increase in the debt limit.