Could be a lot of reasons but it would boil down to backroom deals. Maybe mutual assured destruction, maybe manipulated by someone (everyone talks about how easy he is to manipulate), or maybe a foreign leader has his fingers in the pie and told him to. Hell, maybe they've got underage women in common and Trump didn't want it coming out. The guy is one of Florida's reps and we all know where Trump lives.

My assumption is that he wouldn't have had to resign until there was an official confirmation process, and certainly not before Trump is sworn in. Anything could happen between now and then.