A forthcoming paper in American Politics Research suggests that health reform may have cost the Democrats their House majority in the 2010 election, by making them seem more ideologically distant from constituents in swing districts.

Brendan Nyhan, Eric McGhee, John Sides, Seth Masket and Steven Greene analyzed how Democratic supporters of the health reform law fared in the last round of House elections. They found that, on average, “the vote share of Democrats who supported health care reform was 5.8 points lower than that of the most comparable Democrats who opposed the bill.”

If those Democrats had voted against the law - and flipped that 5.8 percent in the opposite direction - the party would have netted 25 more seats. And that would have been enough to keep the Democrats in a majority.

The authors also probe how, exactly, the health reform law turned voters against some Democrats: It made voters feel more ideologically distant from their representatives. Conservative voters were likelier to view a Democrat who voted for health reform as more liberal than one who opposed it:

Controversial roll call votes—or, more likely, the publicity that they generate in the news media and in campaign communications—can shift constituents’ perceptions of their representative’s ideology. In 2010, Democratic supporters of health care reform were perceived as further to the ideological left, which made them seem more distant from most of their constituents, especially independents and Republicans.

Jonathan Chait questions whether whether these findings indict the health reform law as the culprit in the Democrats’ loss of power. Even if members had voted against the health reform law, he argues, voters may have looked to a separate Congressional vote as evidence of legislators leaning too far to the left.

“If the House had voted down health care reform, some other issue would have become the ‘big vote’ and, probably, have become the proxy for out-of-control liberalism,” he writes. “There could have been renewed attention to stimulus, cap and trade or many new things.”