By Jeff Mason

WASHINGTON (Reuters) - Legislation to allow student loan borrowers to refinance at lower interest rates failed to clear a procedural hurdle in the U.S. Senate on Wednesday, dooming a measure that was a Democratic priority ahead of November congressional elections.

Democrats had said the bill would let holders of both federal and private undergraduate loans - some with rates of 9 percent or higher - to refinance at 3.86 percent. Republicans thought the legislation was too expensive.

The bill, championed by liberal-leaning Massachusetts Senator Elizabeth Warren, was part of Democrats' plan this year to rally their base supporters ahead of an election that could tip control of the Senate back into Republican hands.

Young people made up a huge part of the coalition that helped elected President Barack Obama in 2008 and 2012.

Obama signed an executive order on Monday making it easier for up to 5 million people to pay off college tuition debt and scolded congressional Republicans for opposing the legislative fix to lower student-loan borrowing costs.

The Senate voted on Wednesday 56-38 to end debate on the measure and move to a final vote, short of the 60 votes required for it to move forward.

"It’s a real shame Republicans are standing in the way of this very important, timely legislation," Senate Majority Leader Harry Reid told reporters after the vote.

Republican opposition has thwarted other Democratic priorities, including a push to raise the federal minimum wage and renew expired long-term jobless benefits for millions of Americans.

Democrats control the Senate, 55-45, but need 60 votes to clear Republican procedural hurdles.

Last year, Congress approved the Bipartisan Student Loan Certainty Act of 2013, which set the undergraduate student loan interest rate at 3.86 percent for the current school year.

Democrats proposed that the cost of the bill be offset by reducing tax breaks for millionaires and cited data showing that student-loan debt grew by $31 billion from January to March, to total $1.1 trillion, making it the fastest-growing household debt category.

(Reporting by Eric Beech and Patrick Temple-West; Writing by Jeff Mason; Editing by Caren Bohan and Cynthia Osterman)