The 64-34 vote in the Senate on Thursday sends the measure to President Barack Obama, who has said he will sign it into law.
The legislation would temporarily suspend the $16.4 trillion limit on federal borrowing. Experts say that would allow the government to borrow about $450 billion to meet interest payments and obligations like Social Security benefits and government salaries.
Calculations by a Washington-based think-tank , the Bipartisan Policy Center, indicate that the deadline for Congress to act again to prevent default would likely not come until August.
The Republican-controlled House passed the legislation last week.