Congressional Republicans on Thursday outlined new ways to break the political impasse that threatens to drive up student loan rates July 1.

The proposal came in the form of a letter to President Obama, who has urged Congress to find an agreement that would prevent federally subsidized loan rates from jumping to 6.8 percent from 3.4 percent. The increase would cost 7 million college students an average of $1,000 if no deal is reached.

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

Leaders in both parties have expressed support for keeping loan rates low for another year, but they have disagreed on how to offset the $6 billion price tag.

Boehner challenged

The letter came just hours after House Speaker John A. Boehner (R-Ohio) told House Republicans in a closed-door meeting that he did not expect a congressional deal on the issue before rates double next month. But he assured members that a recalcitrant Democratic Senate would be to blame for the impasse.

At the 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 one person who attended.

A White House spokesman offered a tempered reaction.

“Earlier today, Speaker Boehner reportedly told his Republican colleagues that he thought this was a ‘phony’ issue,’ ” said White House spokesman Matt Lehrich. “Now, he’s signed onto a letter asking the administration to work with him on a legislative fix.”

A spokesman for House Minority Leader Nancy Pelosi (D-Calif.) was more critical of the Republican offer, calling it “a complete and utter ruse” designed to mitigate damage caused by Boehner’s private remarks to his colleagues.

The Republican letter — drafted by Boehner, with Senate Minority Leader Mitch McConnell (Ky.), House Majority Leader Eric Cantor (Va.) and Senate Minority Whip Jon Kyl (Ariz.) — offered the first sign of progress in weeks.

The letter advanced ideas that many Democrats oppose but variations of which have been put forward by the White House in the past.

Two approaches

Two alternatives were offered for paying for the student loan freeze. In one, the costs would be offset by increasing the amount paid by federal employees for their retirement.

In the other, a freeze on loan rates would be paid for through a combination of items: shortening the period during which part-time students would be eligible for federally subsidized loans; limiting the ability of states to recoup Medicaid costs through taxes on providers, which would lead to a slight reduction in Medicaid use and, therefore, lower costs to the federal government; improving coordination with states and local governments to reduce Social Security overpayments.

Obama has been campaigning on college campuses across the country, stressing the importance of congressional action on student loans, an issue that the White House sees as having special appeal to young voters and their middle-class parents.

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