Republicans blamed Democrats for the impasse and suggested that they were manufacturing a political controversy instead of working out differences in private.

“We all agree we’re not going to let the rate go up,” Mr. McConnell said.

The vote was the Senate Republicans’ 21st successful filibuster of a Democratic bill this Congress, which started in January 2011. Republicans have blocked consideration of President Obama’s full jobs proposal, as well as legislation repealing tax breaks for oil companies, helping local governments pay teachers and first responders, and setting a minimum tax rate for households earning more than $1 million a year. Republicans say the measures were flawed and potentially harmful to the economic recovery.

But the student loan filibuster may be the highest-profile stalemate yet, because unlike those earlier bills, this one is not likely to be abandoned. Mr. Obama has elevated the issue by hammering Republicans on it for weeks. American students took out twice the value of student loans in 2011, about $112 billion, as they did a decade before, after adjusting for inflation. Over all, Americans now owe about $1 trillion in student loans. In 2010, such debt surpassed credit card debt for the first time.

The bill in limbo addresses only part of that burden. Graduate students with Stafford loans pay a higher rate, as do students with unsubsidized Stafford loans. Most undergraduates take out both unsubsidized and subsidized loans.