When you strip away all the noise, and the posturing from both Democrats and Republicans, sources on both sides, including in the White House, acknowledge that there’s really only one way out of the impasse.

Both sides have to agree on a way of separating the debt ceiling hike, or hikes, from the process by which spending gets cut — in essence putting an end to a situation in which the debt ceiling is being used as a Sword of Damocles hanging over the spending process. Accomplishing this overall policy goal in a way that can pass both Houses of Congress is the only real way out of the trap right now. The cuts have to be deep enough to pass the House, but the proposal to hike the debt ceiling has to simultaneously satisfy the White House and Democrats.

According to a source close to the talks, Vice President Joe Biden has been in discussions with multiple officials on the Hill from both parties, about ways of realizing this aim.

One idea being floated in multiple private discussions would in effect be a fusion of the Boehner plan and the original McConnell plan to transer control of the debt ceiling to the President.

The idea would be to preserve the joint commission that Boehner’s plan sets up, and also preserve the spending cut targets in Boehner’s plan. But rather than have those tied to two debt ceiling hikes, the President would have the power to hike the debt ceiling unilaterally in keeping with McConnell’s plan, unless a two-thirds veto-proof Congressional supermajority disapproved of it (which wouldn’t happen). The spending cuts in Boehner’s plan would instead be enforced by some kind of trigger — if the committee didn’t reach the goals, automatic cuts of some kind would be triggered automatically.

It can’t be stressed enough that these ideas are far from official proposals and are only several of many that are being batted around. “There may not be enough time on the clock to do something like this,” the source familiar with discussions says. And we still don’t even know whether Boehner can get anything like this through the House.

The trigger idea is also being discussed informally by Senate Dems. Sam Stein reports that once the Senate defeats Boehners’ bill in the Upper Chamber, Senate Dems may approach McConnell and Boehner with various trigger proposals.

Again, these ideas are in flux, are nebulous, and are far from being anything official. But the intensity with which officials are thrashing around for some kind of solution right now is a clear indication of just how deep the quicksand is at this point.

In the end, it’s hard to see how you solve the problem without separating the debt ceiling hike, or hikes, from the spending cuts. And that’s what officials are quietly groping towards as we speak. Whether they get there, of course, is another question entirely.