Gingrich kind of has to go. His name has just started to spike in the polls so he has to try and ride the wave as far as it will go. I am sure his handlers know that he is going to get hammered as a man who cheated on two wives, corporate lobbyist, flip flopper .... etc so he needs to get busy.
Trump is just a media whore. It's what he does. It is no surprise that he interjected his name in to the political arena. There is a lot of money to be made in politics and it boost his already over inflated ego. Win win for him.