WASHINGTON — Senate Republicans on Wednesday blocked legislation aimed at letting people refinance their student loans at lower rates, an outcome that gave Democrats a fresh election-year talking point against the GOP.

The 56-38 vote fell short of the 60 that would have been needed to advance to debate on the measure by Sen. Elizabeth Warren, D-Mass. Her bill would have let millions of borrowers, some with years-old debt and interest rates topping 7 percent or more, refinance at today’s lower rates.

Democrats proposed paying the $55.6 billion price for the lower rates with a federal tax increase on people who make more than $1 million a year.

“With this vote, we show the American people who we work for in the United States Senate: billionaires or students,” said Warren. “A vote on this legislation is a vote to give millions of young people a fair shot at building their future.”

Unlimited Digital Access. $1 for 4 weeks.

Republicans said the bill would not have done anything to lower education costs or reduce borrowing, and they accused Democrats of playing politics by highlighting an issue that was bound to fail.

Sen. Lamar Alexander, R-Tenn., ranking member of the Senate Committee on Health, Education, Labor and Pensions, dubbed the payment mechanism a “class-warfare tax.”

Republicans also pointed to a report from the Congressional Research Service that found the legislation would amount to an average of $1 a day in savings for those with student-loan debt.

“College graduates don’t need a $1-a-day tax subsidy to pay off their loan; they need a job,” Alexander said.

Washington’s senators, Maria Cantwell and Patty Murray, both Democrats, were co-sponsors of the measure.

Student-loan debt has topped $1 trillion and emerged as a drag on the economy and on middle-class families across the country, making it a ripe target for politicians ahead of midterm elections in which Democrats risk losing their Senate majority.

Wednesday’s vote followed two days during which President Obama highlighted the issue, announcing executive action to let more borrowers cap their monthly payments at 10 percent of their income and answering questions about the issue on the social-networking site Tumblr.

The Obama administration said Warren’s bill could have helped some 25 million borrowers save $2,000 each over the lifetime of their loans. It would have allowed people with older loans at higher interest rates to refinance to rates below 4 percent offered today under a deal reached a year ago in Congress.

Three Republicans joined all Democrats in voting to proceed to debate on the bill: Susan Collins of Maine, Bob Corker of Tennessee and Lisa Murkowski of Alaska.

Some 40 million Americans have outstanding student-loan debt totaling $1.2 trillion, making it second only to mortgages in total consumer debt, according to Warren’s office. People 60 and older account for some $43 billion of the total.

Material from McClatchy Washington Bureau is included in this report.