Although the Obama campaign has occasionally sampled this line of attack, they have not yet committed to it. Instead, they have tended to gravitate toward an alternative strategy, painting Romney as a participant in class warfare who will seek to help the rich at the expense of the poor. It's obvious why this strategy is attractive to the Obama campaign: It exploits some of Mitt Romney's weaknesses (being rich, out of touch, etc.), and is a traditional attack made by Democrats.
The class warfare strategy was highlighted by the Obama campaign's unsuccessful attacks against Bain Capital earlier this season. Romney was able to defend his tenure at Bain by pointing to the company's success in saving business and creating jobs. Attacks on Bain aren't the only angle that would appear in the class warfare strategy, however. The strategy would largely depend on creating the general impression that Romney "isn't one of us," and that he only wants to serve the interests of "the wealthiest one percent."
The attacks on Bain also fizzled during the Republican primary. One area where a similar concept did hurt Romney during the primary was his serious gaffe suggesting he wasn't concerned about the poor. When he made the gaffe, Romney was attempting to explain why he was primarily concerned with helping the middle class: The rich are rich, and the poor already have safety net programs designed for them. But the implication Romney didn't care about the poor touched a nerve. It's likely that the gaffe helped weaken Romney in early February, when Rick Santorum won some (temporary) victories against him.
Elephant Watcher's analysis concluded that the class warfare strategy is useful in doing additional damage to Romney, but that the "Bush's Third Term" line would be a better central theme. Why? Though Romney is intrinsically vulnerable to the class warfare strategy, the timing isn't as good as it normally would be. Because Obama is the incumbent in a bad economy, it is Romney who will seek to empathize with those who are suffering. Romney will tend to play up the economic difficulties, and Obama will downplay them. As the challenger, Romney also has the ability to choose what economic policies he will propose. If the middle class believes they would benefit from those policies, it will become even more difficult to see Romney as their enemy. And Romney can also point to the ways in which Bain's investment in companies benefited ordinary workers by creating jobs.
Unless Obama's campaign simply does a better job than Romney's, the result will be ambiguous or even favorable to Romney. Voters want to believe things can get better, and they think it's only possible by going in a new direction--they are unconvinced that a continuation of Obama's policies would lead to improvement in the economy. That's why an ambiguous result to the attacks would be more beneficial to Romney. As long as Romney represents something new (and not obviously dangerous), voters will lean toward him. In other words, Romney wins a draw. Voters don't want to be told they are stuck with the status quo, so they will err on the side of optimism.
Therefore, it makes more sense to undermine the idea that Romney represents anything new at all. If Romney is a return to something that voters already dismissed (i.e. Bush's policies), then the optimistic option is cut off from the beginning. That must be the main goal of the Obama campaign, because if "new" is on the table, voters will probably go with it.
