I don't think he has one. Yes, many liberals are deeply upset right now about his tax cut compromise, and his many other compromises. But as the Washington Post's Chris Cillizza points out, none of this antipathy is showing up in the poll numbers:
While just 48 percent of the overall sample [in the AP's latest poll] approve of the job Obama is doing, 80 percent of self-identified liberals feel the same -- a stratospherically high number. The story is much the same on Obama's personal favorability ratings. [Another AP poll] just after the 2010 election showed that 90 percent of liberals felt favorably inclined to Obama as compared with 55 percent overall.
Theoretically, I suppose, those numbers could change in reaction to the tax cut deal. Legions of disaffected liberals could rise up, abandon Obama, and start ginning up grassroots support for a "Draft Dean" movement. That could be a problem (although after Ralph Nader, I wonder). But I don't think that's going to happen.
I predict that as the 2012 election comes into focus, these angry liberals support Obama with a vengeance. Not just because the race will shape up as one in which these very tax cuts are re-litigated (since they'll be due to expire in 2012), but also because--especially because--there will be a Republican opponent with an agenda that is much more objectionable to liberals. It might even be Sarah Palin.
UPDATE: Greg Sargent, also of the Post, agrees and convincingly posits a gap between the "professional left" and the rank-and-file left.