WASHINGTON — Some senators struggled Thursday to hold together a bipartisan deal to keep student loan rates from resetting to double the current rate July 1.

Top White House officials, meanwhile, told lawmakers they were open to changes in President Barack Obama's student loan proposal if a compromise could be reached that would win congressional approval.

The behind-the-scenes negotiations were an attempt to head off a rate hike that Congress' Joint Economic Committee estimated would cost the average student borrower an extra $2,600. Both parties rushed to microphones to point fingers at the other for the potential hike but kept in touch with back-channel efforts that would prevent them from being blamed for adding to already high college costs.

The bipartisan deal, which would link undergraduate student loans' interest rates with the financial markets, would save the government more than $8 billion over the next 10 years, according to an unpublished Congressional Budget Office report. Democratic and Republican Senate aides insisted on anonymity in discussing the budget office report because it has not been released to the public yet and they were not authorized to discuss it publicly. The compromise plan was similar to one Obama included in his budget and House Republicans passed. That put pressure on the Senate, where a competing partisan proposal came up short last week.

The new bipartisan proposal's $8 billion sum was unlikely to win much support from Democrats, who insist that student loans should not be a source of profit for the government. Students loans issued this year were set to bring in $51 billion net gain over the next decade.

The projections, though, could win votes from Republicans who do not want the popular student loan programs to add to the deficit.

Senate aides involved in the bipartisan negotiations suggested the plan could be revised to make student loans less profitable but still not add to the deficit.

Separately, White House chief of staff Denis McDonough, education adviser Miguel Rodriguez and deputy Domestic Policy Council director James Kvaal met with lawmakers Thursday and told them the White House was open to changing Obama's plan in favor of a compromise that can pass.

“Listen, the president's failed to talk about this issue and he hasn't lifted a finger to push his own party to pass his own proposal,” Republican House Speaker John Boehner told reporters at the Capitol. “The time for games is up. I think our kids deserve better. The president and Senate Democrats need to get their act together so that we can prevent these interest rates from doubling on July 1.”