Photo: John Shinkle/POLITICO

Key players from both sides of the Senate’s student loan debate sat down Wednesday night to hammer out what they hope is a proposal that can finally pass the Senate.

The meeting took place just hours after a failed procedural vote Wednesday on a bill that would have extended subsidized student loan rates at 3.4 percent. The rates had doubled on July 1. Negotiators who backed that bill as well as those behind a competing, long-term proposal huddled for a second time Wednesday in Senate Majority Whip Dick Durbin’s office, capping a whirlwind 24 hours of meetings on the loan issue.

A bipartisan group of senate negotiators agreed to work off the original proposal led by Sens. Joe Manchin (D-W.Va), Angus King (I-Maine) and Lamar Alexander (R-Tenn.) to tie rates for students to 10-year Treasury bill notes, according to a source familiar with the negotiations. But the liberal wing of the Democratic caucus appeared to win a concession from them on capping individual student loan rates, a key sticking point to the current impasse.

The proposal would rewrite all federal student loan rates, creating two classes of loans, one for graduate students and another for undergrads, the source said. All undergraduate students — both subsidized and unsubsidized — would be set at the same rate on a yearly basis. Those rates would be capped at 8.25 percent. Graduate student rates would be capped at 9.25 percent.

Those rates would be higher than the 6.8 percent that subsidized loans reset to on July 1, which could make the bill a tough sell to Democrats who worry such a proposal could end up worse than doing nothing at all. But in the short-term, rates would be well below 6.8 percent. Meanwhile, the GOP has resisted a rate cap beyond consolidated loans.

Negotiators want to make sure the plan would also be deficit-neutral. King said after the meeting that the lawmakers are “waiting for some figures” from the Congressional Budget Office, but declined further comment.

It’s not at all guaranteed the proposal outlined Wednesday will actually pass the chamber; meeting participants must now sell it to their skeptical caucuses to see if there is wide enough support for such a proposal.

The meeting with Durbin on Wednesday night was attended by Sens. Richard Burr (R-N.C.), Tom Carper (D-Del.), Manchin, King and Alexander, all members who have actively been pushing their long-term solution amid objections from most Democrats. Sens. Jack Reed (D-R.I.) and Tom Harkin (D-Iowa) also attended the meeting, representing Democrats who had earlier pushed for the one-year extension.

Many of the same lawmakers huddled Wednesday morning in Durbin’s office, a meeting the Obama administration was briefed in on. Obama’s Chief of Staff Denis McDonough and Education Secretary Arne Duncan met with Senate Democratic leadership on Tuesday night for a 75-minute pow-wow to kick off the furious round of negotiations.