According to Politico, it's likely that the House will vote on the Senate proposal first.

Compromise proposal from the House

Likelihood: Essentially zero

Speed: Slow

This was what the House hoped would happen on Tuesday: Republican leaders would put together a deal in which its warring constituencies each accepted some rollbacks, and then they'd get the Senate and president to go along as the default warning sounded. There is, in some universe, a scenario in which that deal is finally achieved and John Boehner is able to stand in front of a microphone triumphant. That universe is not this one.

Even if the House were able to pull its coalition back together and, unlike Tuesday, develop a proposal that met the needs of 218 Republicans, that bill would almost certainly face fierce opposition on the Senate side and from the White House. After all, concessions to his most stridently conservative base are what got Boehner into this two-week old mess, given that the demands of the Tea Party and the demands of the administration are perhaps as far apart as any two objects in the universe could be.

The House had its chance. Repeatedly. It will not get another.

A stop-gap debt ceiling bill

Likelihood: Low

Speed: Slow

Speaking on MSNBC's Rachel Maddow Show, the National Review's Robert Costa suggested that a last-resort fix could be simply to kick the can down the road for a bit. Boehner "can try to float some kind of six-week extension of simply the debt limit," Costa offered. "I think the leadership would like to embrace the Senate deal. But as we saw today, the way things are so fragile in the House, Boehner may just go for a debt-limit extension."

This morning, however, Costa spoke with Republicans who seemed resigned to going along with the Senate proposal. In other words: a short-term extension could be possible in the worst-case scenario. But for one, that worst-case might actually be avoided.

Passing the existing Senate agreement

Likelihood: Low

Speed: Fairly fast

Remember: The Senate has already passed an unamended bill to fund the government. It did so on September 27. Last week, it seemed poised to pass a clean debt limit increase, though that vote didn't happen — in part due to concerns about obstructionism from Sen. Ted Cruz.

It's unlikely that House Republicans could be convinced to go along with the Senate measure that they spent two weeks rejecting and futilely opposing, but some prominent Republicans — like Rep. Darrell Issa — have expressed a willingness to go along with a full refunding of the government. After all, this is a bill that House Majority Leader Eric Cantor praised in September, given that it locked in cuts from sequestration. Combine this bill with a short-term debt ceiling hike and you've got a plan to avoid default — but, then, you're also basically back at the original Senate proposal.