Top Republican leaders in Congress on Thursday outlined new proposals for how to pay for keeping student loan rates from doubling on July 1, opening new negotiations on the politically charged issue that had appeared to be at a stalemate.

They made the proposal in a letter to President Obama, who has urged Congress to find an agreement that would prevent loan rates from reverting to 6.8 percent from 3.4 percent next month.

Leaders in both parties have expressed support for keeping loan rates low for another year but have disagreed on how to pay the $6 billion pricetag.

The letter came just hours after House Speaker John A. Boehner (R-Ohio) told House Republicans in a private meeting that he expected Congress to be unable to find a compromise before next month — a prediction that drew a sharp rebuke from Democrats.

Boehner said a recalcitrant Democratic-led Senate would be to blame for the rate increase if no deal were reached.

At the closed-door meeting, Boehner characterized the issue as a crisis manufactured by Democrats in a year when the election will be dominated by job creation, according to a source who was in attendance.

The letter to the White House came from Boehner, along with Senate Minority Leader Mitch McConnell (R-Ky.), House Majority Leader Eric Cantor (R-Va.), and Senate Republican Whip Jon Kyl (R-Ariz.).

They outlined two possible alternatives for paying for the student loan freeze. In one, the costs of the lower rates would be offset by increasing the amount paid by federal employees for their retirement. They note that Obama’s budget recommended boosting employee contributions by .4 percent for each of the next three years.

In another scenario, freezing loan rates would be paid for through a combination of lowering the amount of time part-time students could enjoy federally-subsidized loan rates and other items.

“There is no reason we cannot quickly and in a bipartisan manner enact fiscally responsible legislation,” the leaders wrote.

Obama has been traveling across the country, campaigning on college campuses about the need for congressional action.

Rallying his members Thursday, Boehner had noted that the House already passed a bill that would keep loan rates low — a measure that would pay for the $6 billion price tag by eliminating a preventative health-care fund created in the Democrats’ Affordable Care Act.

Democrats oppose the elimination of the fund, and that payment mechanism failed to get the 60 votes necessary to move ahead in the Senate.

A Democratic alternative also failed to advance in the Senate. It would would have paid for the loan-rate cut with a tax change that would have resulted in higher payroll taxes for small business executives making more than $250,000 a year.

It was unclear if the timing of the Republican letter to the White House was in any way connected to Boehner’s remarks to fellow Republicans or to the quick Democratic response to them.

Sen. Charles E. Schumer (D-N.Y.) said Boehner’s comments “confirm our suspicions that Republicans have never been serious about wanting to stop student loan rates from doubling.”

“To many on the hard right, government should not play a role in helping students afford college. Speaker Boehner seems to be following their lead and throwing in the towel on this issue a month before the deadline,” he said.

White House Press Secretary Jay Carney addressed the issue at a briefing, saying that the GOP “thinks that somehow education is not an economic issue. They think education has nothing to do with jobs. The American people don’t believe that. Education has everything to do with employment, with economic growth, with the future of this country.”

But Boehner had told his colleagues that if rates rise July 1, they could always be lowered retroactively if the two sides later arrive at a deal — the point being that the rate issue is important but that Republicans shouldn’t let Democrats use the impending deadline to force a deal that the GOP opposes.

Boehner spokesman Michael Steel said the House “passed a reasonable, bipartisan bill to continue the current student loan rate, as President Obama requested.”

“Senate Democratic leaders have simply failed to do the same. So, if the rates go up, they will obviously be responsible,” he said.