Eric McGhee at The Monkey Cage – a real political scientist who does these sorts of statistical analyses for a living – has done a nice post looking at the 2010 election results, and the effects of the votes for TARP, healthcare, the stimulus, and climate change, on Democrat's electoral prospects.
McGhee correctly objects to analyses (like TfK's) which lump Republicans and Democrats together. Too few Republicans broke ranks on these issues to give statistical insight, and asking the statistical machinery to parse out the effects of four votes within that small group just asks too much of the statistics. He also restricts his analysis to races where the 2008 incumbent is running for re-election, as a fresh Democrat running in an open seat can distance him- or herself from the predecessor's votes. This might be a place where multi-level modelling would help.
McGhee finds a significant effect from the vote for climate change, though a smaller effect than seen for the stimulus or healthcare votes.
When I restrict my analysis to Democrats (but don't restrict myself to 2008 incumbents running for re-election), I get a similar result (excluding TARP, as I haven't got those data handy, and it happened with a different congress). A vote for Affordable Care is the most influential, costing ~5.5 percentage points, followed by ~4.7 points lost for voting for the stimulus. A vote for the climate bill is associated with a slightly significant loss of ~2 points, while a model incorporating interaction terms gets a more significant interaction between district partisanship and voting for the climate bill, In that case, a vote for the climate bill is much more costly in very Republican districts than in Democratic districts, worth about 1.5 points in a district where the presidential candidates were evenly matched, and ~5 points in districts where Democratic presidential candidates underperform Republicans by 5 points. However, that interaction is still only weakly significant. That may reflect the fact that there are relatively few Democrats who voted against any of these bills, and drawing a statistical distinction between any of them gets tricky.
It may well also reflect the simple fact that the climate bill didn't pass. It's a lot easier to demand accountability for a bill that became law than one that died in the Senate. Maybe it would have been a bigger campaign issue otherwise, and we'd see a stronger division between candidates who voted for it vs. those who voted against. Either way, I still think that Democrats didn't lose the House because of the climate bill, and I'm not even sure that vote would have caused Democrats to underperform relative to models incorporating only partisanship and economic conditions. The major hit came from the healthcare vote, and to a lesser extent from the stimulus. Remember, too, that the stimulus brought pork back to some districts more than others, and incorporating ARRA funds spent per district into the model might change some of these results.
Interestingly, if one starts with a model looking for interactions between PVI and each of the three votes, and successively remove the least significant interaction terms, the only interaction that is even barely significant is the one between PVI and the climate bill.
Following the example at the Monkey Cage, I've also counted non-votes as votes against (problematic, as some of those absentees were empty seats). This changes some of the coefficients, but not the basic result. I also have been experimenting with using generalized additive models, which allows variation in the strength of the effect of PVI on % voting Democratic. That also doesn't significantly alter the results, though it does somewhat boost the magnitude of the effect of the climate change vote.