Republicans will try to take credit for it. Voters will reward them by keeping them in the house, while overwhelmingly reelecting Obama over the sh**tty candidate the Republicans are bound to put up.
Ticket splitting is a thing of the past. If Obama wins reelection handily, its almost impossible to imagine the Democrats not regaining the House. If he wins by a small margin, they will probably narrowly keep it. The Democratic percentage of the House vote has tracked identically with the Democratic percentage in Presidential races in Presidential years.