The process of obtaining Justice does have a cost. If the GOP is seen as going after Obama out of spite without any evidence of wrong doing, then they'll pay at the polls.
Right now the stuff you see people say about Obama is the same stuff people said about Bush. It boils down to this: Just because you don't like it doesn't mean its illegal.
A hunt just to try to find politically embarrassing things will be costly to the GOP. If the GOP is serious about this, they need to go in with clearly defined goals of actually broken laws they intend to investigate. A fishing trip won't do it.