Not trying to cop-out of an answer, but it's near impossible to take the context of the show out of this situation. I can't (or don't want to) believe that I live in a world where someone like Frank Underwood could become president with the public being completely ignorant to what he does behind closed doors. We live in a world with "birth certificates" and "swift boating". Certainly, with the enemies list that Frank had made, information would have gotten out.
What you're asking me is contradictory, assume that Frank Underwood exists in the real world, but then assume that government and press that allowed him to operate the way he did in the fictional world, also exist in the real world. It's cognitive dissonance, it makes my brain hurt. It's like what would happen in the real world if Bruce Wayne existed. . . of course people would realize that he's Batman, with the amount of surveillance, even from civillians, the paparazzi would find out in a few weeks . . . .there's just no way no one would know that Bruce Wayne is Batman. No one would even try something like that because the guy that trained him, or flew him to Nepal, would sell out to People magazine in one hot minute.