A top Democrat acknowledged Thursday that President Obama’s health care bill hurt his party in 2010. And a new study suggests it cost the Democrats something pretty specific: their House majority.

“It was clearly a liability in the last election in terms of the public’s fear,” House Minority Whip Steny Hoyer (D-Md.) said Thursday during a briefing with reporters.

House Minority Whip Steny Hoyer (D-Md.) after the House vote on the payroll tax cut extension in December. (REUTERS/Yuri Gripas)

The study ran 10,000 simulations of a scenario in which all vulnerable Democrats voted against the health care bill and found that the rejections would have saved Democrats an average of 25 seats, which would have made the House parties close to a tie. (Republicans won 63 seats overall, but the study suggests around 25 of them would have been salvaged.)

In 62 percent of the simulations, Democrats were able to keep the House.

The study uses district-level data to show that the vote created “ideological distance” between the Democratic members of Congress and the median voters in their districts, compared with similar districts where the Democratic incumbent voted against the bill.

“Democratic incumbents who supported health care reform were seen as more liberal on average by their constituents than those who did not,” the study says.

The study comes at an important time for the health care bill — just as it’s threatening to become a major issue again in the 2012 election.

The U.S. Supreme Court is set to take up a challenge to the individual mandate portion of the bill later this month when it holds oral arguments. Republicans are licking their chops, hoping to rekindle the kind of enthusiasm they reaped from attacking the bill two years ago, just as enthusiasm seems to be on the decline in the GOP.

Democrats, meanwhile, are planning to celebrate the two-year anniversary of the bill’s passage later this month as part of an ongoing effort to make sure the bill isn’t a political liability going forward.

Hoyer said that whatever harm the bill might have caused his party electorally two years ago, the effects are more mitigated now.

“I think some of the fears they had have not been realized,” Hoyer said. ”Therefore, I think you’ve dissipated the opposition. Republicans are going to use it, but I don’t think it’s as fertile soil as they had two years ago.”

The health care bill, in many ways, is a kind of sleeping giant. But it’s about to be awakened, and how the parties navigate the issue in the coming weeks and months will go a long way toward determining how the 2012 election pans out.