The Senate held two votes Thursday on measures to ensure that student loan rates for millions of college students do not double in July — and at the conclusion of the legislative action, the issue remained exactly where it began: stuck.

The measures, one offered by Democrats and the other by Republicans, each failed to reach the 60-vote threshold necessary to move forward, as the parties remain at loggerheads over how to pay for the $6 billion loan subsidy.

If they cannot resolve the dispute, loan rates will rise from 3.4 to 6.8 percent on July 1, increasing the cost of college for 7 million students.

Leaders in both parties have said they want to freeze rates for another year. President Obama has barnstormed college campuses arguing for lowered rates. Mitt Romney, the presumptive Republican presidential nominee, has said he agrees that Congress should extend the lower rates.

But as with many issues in Washington, agreeing on the end goal has so far not been enough to get a bipartisan bill.

Democrats have proposed paying for the additional year of loan subsidies by ending a tax provision that allows executives of some small businesses to collect some of their income as business profits instead of wages, allowing them to avoid paying payroll taxes.

Democrats say the provision is primarily used by professionals such as lawyers and consultants, and they sought to end its use by those making more than $250,000 a year.

Republicans said the Democrats’ proposal amounted to a tax increase on those best positioned create jobs in the sluggish economy. They also argued that payroll taxes are earmarked to fund Medicare, and any new revenue should go to the retiree-health program.

On a 51 to 43 vote, the measure failed to advance.

The Republican proposal would have paid for the loan-rate freeze by eliminating the preventative health-care fund created in the 2010 health-care act.Republicans call it a slush fund and have pointed to what they say are misuses in its spending. Democrats note that it funds HIV/AIDS screenings, obesity prevention and other key programs that could help bring down health-care costs.

The Senate Republican bill mirrored a measure adopted last month by the GOP-controlled House. Republicans called the House action a bipartisan vote and said their Senate colleagues should move forward with the bill. Thirteen House Democrats had joined 202 Republicans in supporting it.

The White House has said Obama would veto that bill if it advanced, but it failed to move ahead in the Senate on a 34 to 62 vote.

There had been no suspense over the outcome of the day’s votes in the Senate — they were staged largely so both sides could point to their own votes in favor of lowering rates while highlighting the opposition’s vote against it.

Democrats say the failure to find a compromise is a sign that Republicans do not actually want to freeze rates. Eliminating the health fund, they argue, is a poison pill that Republicans know Democrats can never support.

“The Republican proposal is paid for by stripping Americans of life-saving preventive health care,” said Senate Majority Leader Harry M. Reid (D-Nev.). “The Democratic proposal is paid for by closing a loophole that allows wealthy Americans to dodge their taxes.”

Republicans countered that Democrats are more interested in finding a popular campaign issue for Obama than working out a solution to the loan issue.

“This problem could have been solved weeks ago,” Senate Minority Leader Mitch McConnell (R-Ky.) said. “Democrats weren’t interested. They wanted a scapegoat more than a solution.”

McConnell called on Obama to become more involved in negotiations to find a resolution to the dispute. “As with so many pressing issues, the president has not led on this issue. He has campaigned on it but has not worked to actually fix it,” he said.

The Senate will be on a one-week recess next week for Memorial Day, while the House returns from a one-week break. The two chambers will likely turn their attention to attempting to negotiate a deal on the issue later in June.