Republicans win if the Bush tax cuts get made permanent, and they win if the tax cuts expire. If its the former, Republicans get their preferred policy option. If it's the latter, they get to accuse Obama of raising taxes. The way the White House really loses politically is if the tax cuts simply expire, since even if the White House capitulates to Republicans on making all the tax cuts permanent the administration gets to claim they worked with Republicans to cut taxes.
But because Republicans win either way, they have no incentive to compromise, and can simply hold out for whatever they want. The more willing to negotiate the White House appears, the more likely Republicans are to move the goal posts. As with health-care reform, Republicans are left with the stronger negotiating position because they're willing to shoot the hostage. The deficit doesn't matter, and even preserving tax cuts for the wealthy comes second to the Republicans' primary goal, which is to destroy the president.
So yes, if the Bush tax cuts expire, they will hammer Obama for it until he's gone. The only way Obama wins this game is to change the game completely, that is to continue his attacks by saying now that Republicans plan to shoot this hostage as Serwer puts it and are willing to raise taxes on 98% of America in order to keep tax cuts on the richest 2%.
That of course would mean Obama would have a different and more effective White House messaging shop, one that calls the GOP out on its economic extortion and does it repeatedly.
That of course is not going to happen.