Even if Boehner and Obama can reach a compromise, Obama will need to decide whether no deal at all is better than the type of deal that might make it through the House — something with less tax revenue and more spending cuts than Obama believes he should have to accept. For example, if Obama is going to raise the income threshold, he would want more in return for such a concession, and there’s no really no way he could wring out more from Boehner.

The White House’s best hope is that Boehner takes a drastically different course and breaks with his own allies. He could decide to negotiate the best bipartisan package possible and put it on the floor with unanimous Democratic support and the backing of Republicans who want to avoid the cliff.

But there’s little expectation that he’ll go that route and weaken his already shaky hold on the speakership. Boehner would flout the “majority of the majority” policy, which was instituted a decade ago by former House Speaker Dennis Hastert (R-Ill). It means that leaders do not put a bill on the floor unless it has the support of a majority of the majority.

“If Boehner keeps insisting on majority of the majority, we go over the cliff, since it’s now clear nothing but a straight-up tea party bill can pass the house under those conditions,” a senior Democratic Senate aide said…

But the White House has to be worried that at some point, the public questions will turn to Obama’s stewardship of the process, and that’s where Boehner’s weakness is troublesome.