According to polls from ABC/Washington Post and Pew, the deal Obama struck with congressional Republicans is pretty popular, earning a majority in the Pew poll even among self-identified liberals and Democrats. The former poll finds 69 percent support the package, while the latter poll finds 60 percent approve.
That doesn't surprise me -- the fact is the Democratic and Republican coalitions are pretty different, and one of the ways they're different is that Democrats are far more supportive of their leaders compromising to achieve goals, whereas Republicans are more inclined to want their leaders to "stick to their beliefs" even if that means nothing gets done.
That may be because Democrats actually want to get things done and Republicans are happy to scream "stop," and because Democrats as a party are more dependent on the support of moderates and conservatives than the GOP is on liberals. Given the nature of the two coalitions, the popularity of the deal among Democrats makes sense.
My biggest worry has been that the payroll tax cut is, as David Dayen has written, a way for Republicans to undermine Social Security. Tim Fernholz points out that the idea has been bouncing around liberal circles for some time, and Republicans are going to attack Social Security no matter what.