Romney has two, and exactly two, qualifications to be President. One is his term as governor of Massachusetts. But the one actual accomplishment of his time in that office, Romneycare, is something he must by necessity run away from. So he's left with running on his record as a businessman. This is his one and only claim to the office. Without that, he's just some schlub off the street pitching an amalgamation of Paul Ryan and George W. Bush. This is different from the attacks on Obama's relationship with Rev. Wright, as Wright was not central to Obama's purpose for his candidacy.
At the very least, in the last few days, the Obama campaign has managed to make Bain a question mark in voters' minds. His time there was not all successful investments and good management; there was some Gordon Gekko in there. In addition to blunting the biographical advantage of Bain, this whole affair has solidified the concept of Romney as rich guy, which will be damaging for the GOP as previously discussed.
Romney is singularly unable to get away from this issue, despite the beating he's taken over the last few days, because he has nothing else to run to. He wants to return focus to the economy, but the only reason anyone cares what he has to say about the economy is his Bain record. And his best defense his time as CEO is that he's a sort of financial Mr. Magoo, blind to the results of his underlings' machinations. It's not a powerful position to be in.