If, by your own loudly touted standards, you have betrayed the trust of your followers and are in disgrace according to those standards, then you should resign. A leader who cannot live according to rules he enforces on others, but still refuses to resign, is a person who has no standards at all, an empty corpse of ethical browbeating leaving itself to rot in the public arena. Whether the standards are those of sexual conduct, business ethics or honesty in government, a standard I don't agree with but which others conscienciously live by deserves my consideration.
I don't need to list the many failures of public figures to live up to standards to which they harshly hold others: you haven't got all day to read blogs. And to those few who have done the right thing after having done the things they say are wrong, my condolences and appreciation.
A standard that exists primarily as a lie on the lips of officials makes, by association, liars of us all.