This is never the case. I was working in congress when the Anthony Weiner scandal hit. Behind the scenes it was absolute chaos and he almost had to be frog marched out of the capitol by the Democratic leadership. True, there was no legal requirement he resign. He could've easily said screw you, impeach me like Trafficant, but the pressure to go is immense. Mark Foley locked himself in his office sobbing, and was so inconsolable that his Chief of Staff had to hold his hand (literally) while he singed the resignation letter.