On stage, Nixon portrayed Juliet in a 1988 New York Shakespeare Festival production of Romeo and Juliet and acted in the workshop production of Wendy Wasserstein's Pulitzer Prize-winning The Heidi Chronicles, playing several characters after it came to Broadway in 1989. She replaced Marcia Gay Harden as a pill-popping Mormon wife whose husband reveals his homosexuality in Tony Kushner's landmark two-part Angels in America (1994), received a Tony nomination for her performance as the headstrong young woman who falls for a mama's boy in Indiscretions (Les Parents Terribles) (1996, her sixth Broadway show) and, though she originally lost the part to another actress, eventually took over the role of Lala Levy, the aspiring Scarlett O'Hara in the Tony Award-winning The Last Night of Ballyhoo (1997).

Nixon was a founding member of the theatrical troupe The Drama Dept., which included Sarah Jessica Parker, Dylan Baker, John Cameron Mitchell and Billy Crudup among its actors, appearin