WASHINGTON — Democrats and Republicans alike say they want to prevent the cost of federal loans from ballooning for millions of students. But the effort has evolved into an election-year battle each side is using to embarrass the other and spotlight its own priorities to voters.

In the latest political chess move, Speaker John Boehner, R-Ohio, scheduled a House vote for Friday on legislation preventing the 3.4 percent interest rate on subsidized Stafford student loans from doubling as scheduled on July 1. In a bitter pill for Democrats, the measure’s $5.9 billion cost would be paid for with cuts from President Barack Obama’s health care overhaul bill.

Boehner announced the vote in an abruptly called news conference Wednesday that followed days of pounding by Obama and congressional Democrats. It also came two days after the GOP’s presumptive presidential candidate, Mitt Romney, tried defusing the issue by embracing the call for freezing interest rates, putting more pressure on congressional Republicans to back the effort or look isolated.

“What Washington shouldn’t be doing is exploiting the challenges that young Americans face for political gain,” Boehner said. He also accused the president of “campaigning and trying to invent a fight where there isn’t and never has been one.”

Congressional GOP aides said Republicans were working on the legislation for some time and unveiled their bill to try to prevent Obama from escalating the dispute. The aides spoke on condition of anonymity to discuss party strategy.

Hours before Boehner spoke, Obama wrapped up a two-day trip to three college campuses in which he cast himself as the students’ champion and Republicans as the ones standing in the way of resolving the problem.

“How can we want to maintain tax cuts for the wealthiest Americans who don’t need them and weren’t even asking for them?” Obama said at the University of Iowa, mocking the GOP. “I don’t need one. I needed help back when I was your age.”

The backdrop to the student loan fight is a push by both parties to appeal to younger voters, an Obama strength in his 2008 election win, and to signal their sensitivity to families’ struggles during the economy’s prolonged slump. Letting the loan rate double this summer would cost 7.4 million Stafford loan recipients an average $1,000, according to the administration.

At the same time, each side wants to force the other to take politically uncomfortable votes.

The House GOP bill is paid by cutting health care programs Democrats treasure. The Senate Democratic version would force high-earning owners of some privately owned corporations to pay more Social Security and Medicare payroll taxes, violating Republicans’ anti-tax doctrine.

The House GOP bill would cut a $17 billion prevention and public health fund Obama’s law created for immunization campaigns, research, screenings and wellness education. Republicans have dubbed it a “slush fund” and sought to cut it to finance a variety of projects, succeeding earlier this year to help pay for maintaining doctors’ Medicare reimbursements.

“Rather than letting student loans become a pawn in the latest political fight, the House will show our commitment to our nation’s students and extend the current rates without adding a dime to the deficit,” said House Majority Leader Eric Cantor, R-Va.

It didn’t take long for the measure to stir up opposition among Democrats.

“We should be able to work together to find offsets that don’t penalize middle-class families or undermine efforts to help more Americans stay healthy,” said White House spokesman Nick Papas, who expressed confidence that a compromise could be reached.

Rep. George Miller of California, top Democrat on the House Education Committee, accused Republicans of trying to keep student interest rates low by “extracting the price from women and children.”

House Minority Leader Nancy Pelosi, D-Calif., a supporter of the health fund Republicans targeted, said the GOP had made “a dramatic reversal” because Republicans had recently pushed a federal budget through the House that would have let student interest rates double. But her statement stopped short of saying she would oppose the GOP bill on Friday.

Senate Majority Leader Harry Reid, D-Nev., said Democrats opposed cutting the health program “just so Republicans can continue protecting millionaire tax dodgers.”

That reference was to his own legislation, which would pay for keeping student loan interest rates level for a year by forcing high-income owners of some privately held corporations to pay more Social Security and Medicare payroll taxes.

Senate Republicans say they support freezing students’ interest rates but have strongly opposed boosting those companies’ payroll taxes.

“Democrats want to pay for it by raiding Social Security and Medicare, and by making it even harder for small businesses to hire,” said Senate Minority Leader Mitch McConnell, R-Ky. “We happen to think that at a time when millions of Americans and countless college students can’t even find a decent job, it makes no sense whatsoever to punish the very businesses we’re counting on to hire them.”