The Democratic Party contains much larger ideological fissures than the Republican Party, and one of those fissures is that the Obama administration favors cuts in Social Security and Medicare spending that liberal Democrats don't like. Part of Obama's strategy for maintaining Democratic Party unity as he pursues his fiscal policy agenda has been to take advantage of the fact that these same liberal Democrats generally believe that taxes—especially on the wealthy—are too low.
So part of the hypothetical "grand bargain" is that Obama gives Congressional Republicans spending cuts that they want in exchange for giving him revenue increases that he wants. But another part of the hypothetical grand bargain is that liberals give Obama spending cuts that he wants as part of a package deal that includes tax hikes that liberals want.
And even as Obama muses about fiscal cliff dynamics giving him leverage over the GOP to get a grand bargain his objective leverage over liberals is waning. As I wrote in my piece making the case for leaping off the fiscal cliff, once the New Year begins the idea of a taxes-for-cuts bargain becomes irrelevant. With the Bush tax cuts fully expired, taxes will be higher than Obama wants as well as (much) higher than Republicans want. The relevant tax bargain will then be between Obama and the GOP over how much to cut taxes. Whatever the outcome of that agreement, it leaves you with nothing to take to liberals in exchange for spending cuts.
Indeed, part of the perversity of the 2011 grand bargain negotiations is that all the talk of "new revenue" was relative to the current policy baseline (i.e. with the Bush tax cuts) rather than the current law baseline in which they expire. Obama was offering spending cuts in exchange for the GOP affirmatively agreeing to lower taxes than would be locked into place in the absence of an agreement. That was well-suited to both Obama's substantive views on the budget and to his clear preference for bipartisan dealmaking as such.
But the closer we get to the actual fiscal cliff the less sense it makes as a genuine bargain for people who think Social Security and Medicare cuts are bad on the merits. That's why you see things like AFL-CIO President Richard Trumka loudly hopping off the grand bargain bandwagon. It's not clear to me how much this substantively matters. The left-wing of the Democratic caucus rarely gets its way on anything. But the political system has an enormous inaction bias built into it, and objectively speaking the incentive for liberal wing of the Democrats to sign on to a grand bargain is vanishing fast.