As Paul notes below, Jon Chait argues that a Republican-controlled House will impeach Obama (although they would have no chance to remove him from office). First of all, Chait does address Paul's response in the subscriber-only section:
The Republicans wouldn't dare repeat the mistake they made by impeaching Clinton, you say? You're not thinking like a Republican. In the conservative mind, the impeachment crusade was not a political miscalculation but a misty, watercolored memory. ... In this interpretation, the process sufficiently tarnished Clinton so that his vice president was unable to run on the administration's accomplishments and was easily tarred as a liar during the crucial stretch in October 2000 when the media pounced upon Gore's veracity.
I can't say with any confidence who's right about the politics here, but I can bring some potential evidence from political science. Yale political scientist Stephen Skowronek generated a significant amount of attention (although not nearly as much as his work merited) by predicting that Bill Clinton would be impeached ... in 1993. This was based on his theory of presidential politics, which evaluates presidents in relationship to the dominant political regime. Clinton was at severe risk because he was a "preemptive" president, working within a political regime defined by the other party. And while of course not all such presidents are impeached and some (with Eisenhower being the foremost example) are even politically successful, the risk that they will end up in the crosshairs of Congress is high.
What does this tell us about Obama? Well, if history holds this would tend to support Paul's skepticism. The 2008 election seems much more like a "reconstructive" election than a "preemptive" one, and (as Clinton found out) the Affordable Care Act isn't the kind of thing that generally passes during the politics of preemption.
I wouldn't, however, say that Chait's prediction is as implausible as this implies. The first possibility is that in retrospect we may see Obama as another preemptive president in a political regime still defined by Reaganism. I don't think this is likely, although it can't be dismissed entirely (as recently as five years ago something like the ACA was acceptable to many conservatives, and if Republicans carry the White House in 2012 and get a stranglehold on the Supreme Court ...) The more likely possibility is that -- while the patterns he's discovered have been remarkably robust -- Skowronek's theory is finally breaking down. Each "reconstructive" president effects less radical change than the previous one, and we may be at a stage of American politics where a reconstructive presidency in anything like the mold of FDR just isn't possible, and so Obama doesn't really fit into any recognizable category. If so, all bets are off. If I had to bet, I would say that Obama will not be impeached -- but Chait could well be right. History may not offer much guidance for our current political situation.
--Scott Lemieux