When Martha Johnson thinks back to that Monday in April 2012 when she resigned as head of the General Services Administration, she remembers a day as still as the hands on a broken clock. She had spent the weekend practicing her resignation speech in front of the mirror. She repeated it over and over until her face had memorized how to form the words without twitching. Until her voice could say it without warbling. Until her eyes could stop all that blinking. Finally it was time. She walked into the 2 p.m. senior staff meeting at the GSA, gave her...