Mitt Romney might or might not cave and release more than the two years of tax returns he’s promised; and whatever his decision, it might or might not damage his White House prospects.

The more than half-dozen Republican strategists I spoke with in the days since President Barack Obama accelerated his attacks on the presumptive GOP presidential nominee’s business career were split on how much influence this issue would have outside the Beltway among the voters who will decide the presidential election. Voters are notorious for ignoring “game-changing” campaign attacks that Acela Corridor experts are convinced will have a major effect.

But on one element of Obama’s criticism of Romney, and the former Massachusetts governor’s response, there was virtual unanimity: He must talk more about his tenure at Bain Capital — and he has to do so willingly, proudly and enthusiastically. Either that, or he allows Obama to define a major portion of his life negatively and he cedes his business experience as reason to elect him in a contest that is about who can best create jobs.

“Romney needs to turn his time in the private sector into a positive on job creation and having exactly the skills needed right now to get this economy firing,” said one unaffiliated Republican consultant who lives and works in a presidential battleground.

Unlike many Republican operatives based in Washington, D.C., this consultant was not hyperventilating about Romney’s defensive and seemingly unprepared response to Obama’s attacks on his tax returns, when he departed Bain Capital and whether, as leader of that firm, he was responsible for the outsourcing of U.S. jobs.

But this GOP adviser suggested that withstanding Obama’s attacks, as Romney appears to have done for now, according to recent polls, and simply riding a bad economy to victory by running out the clock is insufficient. Romney has to give voters a reason to both fire Obama and hire the challenger — and talking about how Bain informs his ability to turn things around should be an integral part of his sales pitch.

“Hits like this raise some doubts with blue-collar folks and independents and keeps them from jumping ship [from Obama],” said the Republican consultant, whose roster of clients includes Congressional candidates. “The next push should be Romney’s. If he can start a march, he might just move ahead in key states.”

For more than a year, Romney has touted his business background as among the top reasons to trust him with the Oval Office. His central attack on Obama is that when it comes to leading an economic recovery, he’s out of his depth, while the former Massachusetts governor has the right mix of government and business experience to turn things around.

That is why some Republicans are mystified at what appeared to be a tactical failure to respond strongly to Obama’s recent attacks, not to mention the tax returns issue, which Romney endured in the GOP primary. And although even Republican operatives critical of how Romney has handled this episode believe these attacks are unlikely to leave a mark, they worry about the next barrage and the possibility that the accumulation could distract voters from the economy.

But amid the complaints about tactical failures — “This was a direct result of not planning properly,” one D.C.-based Romney supporter told me — the overriding concern in terms of Romney’s chances for success revolve around his treatment of his business career going forward. With Romney still an unknown quantity to many voters, the Republicans I spoke with said it would be a big gamble to dismiss Obama’s attacks as a failed, midsummer waste of time and money.

Bain can and should be a positive aspect of the campaign for Romney, said one Republican operative based on the West Coast. The issue, this individual said, “isn’t just about something Romney did, but who he is and the core of his life experience. They have to argue it back to a draw, that this is what Romney did, he’s not a bad, shady person and he knows how to create jobs.”

Added the operative: “Part of the problem is the character assault and him appearing as though he doesn’t want to explain it.”