An emerging deal to lower interest rates on student loans hit a major obstacle Thursday after lawmakers were told it carried a $22 billion price tag over the next decade.

The proposal was designed to offer Democrats the promise that interest rates would not reach 10 percent and to give Republicans a link between borrowing terms and the financial markets that they sought. But at that cost, the bipartisan coalition behind it decided to hit pause and return to negotiations to bring that cost down.

The estimate was described by a congressional aide involved in the negotiations. The aide was not authorized to discuss the proposal by name and insisted on anonymity because the Congressional Budget Office report had not yet been widely released.

The unexpected cost estimate was unlikely to end talks among lawmakers about how they might reduce rates on subsidized Stafford loans, which doubled to 6.8 percent last week after congressional inaction.

Efforts to restore those rates to 3.4 percent were abandoned in favor of a new compromise that bears many similarities to a bill that House Republicans have passed, and with President Barack Obama’s budget proposal.

“There is no question that there is a compromise available on this important issue and that the sides have not been that far apart and we just need to get it done,” White House spokesman Jay Carney said before the estimate was released.

“We have been working with lawmakers to make that compromise happen. We need to make sure that students don’t see their rates double,” he said.

Under the plan lawmakers were considering, interest rates on new loans would be based on the 10-year Treasury note, plus an additional percentage to pay for administrative costs. The proposal includes a limit on how high rates could climb, a demand Democrats said was a deal-breaker.

That provision proved unexpectedly costly and, for the moment, proved problematic for negotiators.

Undergraduate students would have seen better terms than the current 6.8 percent rate but could have faced higher costs if the economy improves and Treasury notes become more expensive. Rates for students this fall would have been about 4 percent and would have been capped at 8.25 percent in future years.

Graduate students and parents could have found better deals next year but again would have faced higher rates than the current 7.9 percent. Borrowing for those PLUS loans would have been about 6 percent this fall and capped at 9.25 percent in coming years.

Serious work on a compromise came just hours after Democratic-led efforts to restore the 3.4 percent interest rates failed once more to overcome a procedural hurdle in the Senate. After several failures to find a stopgap measure, Democrats abandoned that tactic and instead looked for a way to lower rates for students before their return to campus this fall.

If fresh negotiations prove fruitless, millions of students returning to campus next month will find borrowing terms twice as high as when school let out. Without congressional action in the coming weeks, the increase could mean an extra $2,600 for an average student returning to campus this fall, according to Congress’ Joint Economic Committee.