Here's the biggest problem for the GOP: let's say that tomorrow, another sex scandal breaks in the House, this time involving a Democrat--even a Democrat in the leadership. Would this help of hurt the GOP chances in November?
I would argue that it would just hurt them further, especially among the GOP base. There is a feeling that the House has become a den of corruption, full of politicians who care more about power and money than they do about principles. This is one of those difficult to dispel feelings, because it is based on truth.
I remember seeing comic strips in the 1990's portraying Congress they same way they had in the 70's and 80's, with a bunch of big blowhard Tip O'Neil types, and thinking that they seemed out of date since Congress had become full of reformers and zealots (who sometime went to far, really). But now those comics would seem quite modern. It's a shame, and if the GOP loses control of either or both chambers, it will be deserved.