He is absolutely one of the most pretentious, arrogant politicians ever - and that's saying a lot as New York has bred an enormous number of pretentious, arrogant politicians. He should resign, but won't as he probably only feels he did one thing wrong - he got caught, i.e., the Bill Clinton syndrome.
The media is already trying to cover for him by questioning why prostitution is illegal. I think he made that comment in his so-called apology, yesterday.
The latest talking point will be that he is a victim of an outdated, puritanical mindset that makes a "natural" business illegal.