Matt Yglesias is claiming that POTUS and Congressional Democrats can safely ignore John Boehner: 

To take the bargaining process seriously at this point you have to believe that come 2013, House Republicans would actually refuse to cut taxes on the grounds that the president’s tax-cut proposal doesn’t cut taxes enough. Then they would blame the economic drag and middle-class pain that their own refusal to cut taxes had caused on the Democrats. But that doesn’t pass the laugh test as a political argument.
It doesn’t matter whether that argument passes Yglesias’s laugh test.  All the matters is whether it passes the House GOP’s laugh test.  
And if it does–if a substantial majority of the House GOP are comfortable going on talk shows demanding “tax relief for all Americans,” that time-tested (and presumably donor-tested) phrase–then the bargaining game changes completely.  All the House needs to do is vote for a bill giving “tax relief for all Americans” and a good fraction of the House GOP will be able to sleep well at night and a couple of dozen more will just pop a Xanax.  After that, it’s just a matter of which side blinks first.  
Fortunately, recent history gives us an N=1 piece of data on who blinks first when tax cuts for the rich are on the line: Democrats.  You’ll recall that we actually faced a similar tax standoff in 2010, and I’m sure Google can prove that plenty of left of center bloggers told the President that he didn’t need to give in to the GOP’s demands because of some theory of human rationality.  But all the same, the President gave in.  [Insert obligatory reference to Dixit and Nalebuff’s excellent treatment of brinksmanship here.]
And remember, President Obama didn’t even face a GOP-controlled House at that point.  One can detail the differences between 2010 and 2012 but I doubt the differences net out to much.  
Why did President Obama cave in 2010?  Why might he cave today?  What does he (probably) see that the progressive blogosphere (probably) does not?  
The President knows that the GOP isn’t just trying to please the median voter (and I say this as a fan of the median voter theorem). The GOP is also trying to please something like the median Republican, just as  Democrats are trying to please something like the median Democrat.  Each party is a cartel, controlled substantially by the median member of the cartel.  And as long as the median cartel member is happy, there’s some surplus to spread around.  
Cox and McCubbins wrote a fantastic book about this concept of parties as cartels: Legislative Leviathan, a blend of rich institutional knowledge, history, statistics, and public choice.  When I think of parties as cartels, the behavior of the House GOP makes more sense–just as Congressional Democratic votes for ACA made sense.  
And once we think of parties as cartels–organizations that have real-though-often-invisible tools for disciplining their members–we can understand why Representative Weiner resigned: The cartel had power, the power to reward or punish with an invisible hand. 
My prediction: The outcome of the fiscal cliff battle will be reasonably far from President Obama, Majority Leader Reid, and Minority Leader Pelosi’s bliss points.  More formally, it will be outside their Pareto set.   Boehner–a willing compromiser–will ultimately be able to say he kept tax rates on the rich from going all the way back up to Clinton-era levels.  
Coda: Remember that Boehner is open to raising tax revenues from the rich.  That’s a bargaining angle I’m looking forward to watching over the next few weeks.