WASHINGTON - The measure, passed last week by the House of Representatives, would increase the debt limit, now at $12.1 trillion, by $290 billion.
Senate Democrats may approve the measure largely by themselves because most, if not all, Republicans are expected to vote against it, Republican aides said. Democrats control the Senate, 60-40.
Republicans have objected to raising the debt limit, accusing Democrats of reckless spending. Democrats counter by noting that the debt exploded during the administration of Republican President George W. Bush, which ended in January.
Democratic President Barack Obama is expected to promptly sign the debt-limit measure into law after Senate approval.
The Treasury Department has warned that it would likely reach the current debt limit by December 31, potentially putting the United States at risk of default.
U.S. lawmakers want to avoid default but have refused to provide a long-term increase amid mounting concern about the debt limit.
Democratic leaders had hoped to raise the limit by at least $1.8 trillion, enough to ensure they would not have to revisit the issue before the November 2010 congressional elections. But they were unable to agree on measures that lawmakers had hoped to attach to the legislation to control the debt. The two-month hike provides more time to reach a deal.
The government posted a record $1.4 trillion deficit in the fiscal year ended September 30 and is on track this year to spend at least $1 trillion more than it collects.
The debt has more than doubled since 2001, due to wars in Iraq and Afghanistan, tax cuts and the worst recession since the 1930s, one that has caused tax revenues to plunge and spending on federal safety-net programs to rise.
Senate leaders set the debt-limit vote for Thursday, Christmas Eve, just before lawmakers go home for the holidays.
The vote is to occur after anticipated Senate passage of a bill to overhaul the U.S. healthcare system, a measure that has tied up the chamber for weeks, delaying departure.