Douthat believes that the tax deal has made a grand deficit reduction plan before 2012 less likely:

The left-wing angst [over the tax deal] means that for the first time in his presidency, Barack Obama has to worry about liberal disaffection on a significant scale, which makes it hard to imagine him alienating his base still further by taking another plunge into bipartisanship and accepting entitlement cuts before the 2012 election. (A prediction: In the unlikely event that Obama makes a deal to means-test Social Security in the next 12 months, he will face a primary challenger in 2012.) 

Sargent doesn't see a lot of evidence of this in the poll numbers:

On the general question of whether to compromise with Republicans -- and on [the tax cut] deal in particular -- there does seem to be a real gap in opinion between Dem rank-and-filers and Obama's high-profile critics.