President Obama is racing to turn Bain Capital into a liability for Mitt Romney, even as the Republican candidate argues that his track record at the private-equity firm qualifies him to be president.

Obama on Monday published a  new ad starring two former steel workers who say they lost their jobs because Bain bought their company and closed the Missouri steel plant after making money off of it.

Both Romney and Obama are exaggerating parts of the story. Romney's team has argued that Romney isn't responsible for the job losses in question because the plant was shut down in 2001, two years after Romney left Bain. Obama's campaign says Romney is responsible for them because he created the "structure" under which the workers lost their jobs.

The Obama campaign has also drawn criticism from a former White House adviser and fact-checkers, though that doesn't seem to change the reality that most people don't fully understand what private equity is, or how to even measure Romney's success there.

If the Bain debate seems familiar to you, it's because this fight has already been had during the Republican primary. Newt Gingrich led the charge against Romney, calling him a vulture capitalist for buying companies, profiting off of them and leaving them in the dust. Romney responded by claiming that he created 100,000 jobs through his work at Bain.

Financial analysts might have been perplexed as to why Romney made that assertion. Private-equity firms aren't intended to create jobs; their goal is to make money for investors. And Romney's claim itself was dubious - the companies he pointed to that added thousands of jobs did so after he left the firm. His campaign today stands by taking credit for those jobs, even as it says Romney isn't responsible for jobs that were lost after 1999, like those at the shuttered steel plant in Missouri that's the focus of Obama's new ad.

"During Mitt Romney's time at Bain Capital, the firm invested in or helped start up over 100 companies," Romney spokeswoman Andrea Saul said in an email. "If you look at just four of the startups alone, they add up to more than 120,000 jobs - Bain's help under Gov. Romney led to the existence of those companies and, thus, the jobs."

Romney countered Obama today by pushing out his own video about a steel company that he says grew because Bain invested in it. The ad says the company, Steel Dynamics, grew from 1,400 workers to more than 6,000 because of Romney.

Steven Rattner, Obama's former auto bailout adviser, said this morning that the jobs focus is misleading.

"Mitt Romney made a mistake ever talking about the fact that he created 100,000 jobs," Rattner said on TV. "Bain Capital's responsibility was never to create 100,000 jobs, or some other number. It was to make profits for its investors."

Rattner said job losses are "part of capitalism" - a line similar to what Romney has said in defending his time at the firm - and added that Bain performed "superbly well" and acted "responsibly."

Democrats have spurned their turncoat. Democratic National Committee spokeswoman Melanie Roussell responded in an email: "This is exactly the point. He says Romney is wrong to claim his goal was job creation - it wasn't. No one is challenging Romney's right to run his business as he saw fit, and no one is questioning the private equity industry. That's  not what this is about. This is about whether the lessons and values Romney drew from his time as a buyout specialist are the right lessons and values we want in our President."

One reason you won't hear Romney talk about Bain a lot is because it separates himself from real workers in real jobs, not financial speculators and high-powered investors who buy and sell companies. Even if Romney had impeccable success at Bain, few independent voters are able to connect with the idea of running a private-equity firm.

The reality is that Romney more likely than not did a good job at Bain. He's a smart businessman with an ideal upbringing to merit success at a private-equity firm. He'll have trouble explaining why he can claim credit for jobs that were created after he left, but not take the blame for jobs that were lost after he left - what's undeniable is that he and his investors made money during the process, which was their goal.

Obama will also have trouble explaining why Romney is the "vampire," as the new ad says, who sucked the jobs out of the Missouri steel plant two years after Romney left. But it seems clear that Obama's attack on Bain is another arrow he has that's not about his own economic record of the past three years, a point that Republicans seem to be making fairly. A day in which the news media cover Bain instead of the unemployment rate is a good day for Obama, no matter what exactly Romney did while he was there.