Senators voted 46-53 against Warren's amendment to the Republican budget resolution.

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Warren's amendment would have allowed people with college loan debt to refinance at interest rates from the 2013-2014 academic year. The Massachusetts Democrat, who is rejecting calls to run for president, said the move would allow undergraduates to refinance their loans to a 3.9 percent interest rate, with a "slightly higher" rate for graduate students.

"Millions of borrowers are still stuck paying interest rates at 6 percent, 8 percent, 10 percent and even higher," she said.

Her plan would have been paid for by requiring millionaires to pay at least a 30 percent effective federal tax rate.

"The amendment would save borrowers hundreds, if not thousands," Warren said. "We have a choice: protect a tax loophole for billionaires or give millions of middle class people a chance to build some real economic security. ... Congress has worked too long for the billionaires"

unless the Massachusetts Democrat agreed to unlimited amendments. Wednesday's vote isn't the first time Republicans have stopped Warren's student loan efforts. Sen. John Cornyn (R-Texas) blocked a bill from being brought up last year,

Warren said Wednesday that, because of the Republicans' decision, the "student debt problem got worse, much worse."

"Last year, Republicans blocked our efforts to lower student loan interest rates ... so tens of millions of borrowers got nothing," she said ahead of the vote. "While Republicans were busy blocking student loan refinancing, our country's student debt problem got worse, much worse."

Sen. Mike Enzi (R-Wyo.) urged his colleagues to vote against Warren's amendment. The Budget Committee chairman said something has to be done on student loan debt but said the budget resolution wasn't the place for it.

"Addressing college costs and the burden of high student debt loans has to be done, but it can't be done on a budget bill," he said ahead of the vote. "You can't have policy on a budget resolution."

Senators passed by voice vote a separate student-loan related amendment. The amendment, by Sen. Richard Burr (R-N.C.), aims to simplify loan repayment by reducing overlapping programs.