Posted elsewhere, but I'll repeat myself:
What this guy should do:
Call a press conference.
Walk in the door, up to the mike and make this statement:
"Yes, that's me in the picture.
It was a long time ago, when I was younger and more callous than I am today.
I wouldn't do it again.
I will not resign and will continue to serve my duly-elected term.
If you don't like it, you can kiss my a##.
Ladies and gentlemen, that's the end of this press conference."
... and then, walk back out the door.