If you are a craven politician, just don’t resign. “Surviving” a scandal is pretty easy if all you want is to “survive.”
Scandal-plagued people who refuse to resign (David Vitter, Larry Craig, Charlie Rangel, Maxine Waters, et al.) keep their jobs. Furthermore, despite impropriety that the rest of the country dislikes, their constituents don’t seem to mind.
Additionally, party members should not force you to resign, because it actually costs them in the long run. They are much less likely to win the seat after you’ve resigned (see William Jefferson, Chris Lee, and now Anthony Weiner).
Voters reward stubbornness and craven lying. Live up to your reputations, politicians!