I'd have to disagree. I see no point to him resigning. An attempt was made to blackmail him and rather than submit, he revealed the matter on his own. I question his judgment in having an affair, but I am not worried about blackmail. His constituents can determine next election day if his lack of morals should cost him his seat.
If he worked for my company, I’d fire him on the spot, no questions asked.
Well, then, since the job of United States Senator does not require the exercise of judgment, there's no reason he should quit.