He had just flown across the country after an exhausting campaign day in Oregon and South Dakota, landing at the White House after dark. But President Bill Clinton still had more business before bed. He picked up a pen and scrawled out his name, turning a bill into law. It was 10 minutes before 1 a.m. on Saturday, Sept. 21, 1996, and there were no cameras, no ceremony. The witching-hour timing bespoke both political calculation and personal angst. With his signature, federal law now defined marriage as the union of a man and woman. Mr. Clinton considered it a gay-baiting...