Harden was born in La Jolla, California, the daughter of Texas natives Beverly Harden (née Bushfield), a housewife, and Thad Harold Harden (1932–2002), who was an officer in the United States Navy. Harden's brother is named Thaddeus, as are her father and her former husband. Harden's family frequently moved because of her father's job, living in Japan, Germany, Greece, California, and Maryland. Harden graduated from Surrattsville High School in Clinton, Maryland in 1976. She received a Bachelor of Arts in theater from the University of Texas at Austin in 1980. Harden received a Master of Fine Arts from New York University's Tisch School of the Arts in 1988.
Harden's first film role was in a 1979 student-produced movie at the University of Texas. Throughout the 1980s, she appeared in several television programs, including Simon & Simon, Kojak, and CBS Summer Playhouse. She appeared in The Imagemaker (1986), her first movie screen role, in which she played a stage manager. She appeared in the Coen brothers' Miller's Crossing (1990), a 1930s mobster drama in which she first gained wide exposure.
Even so, at the time, living in New York City, she had to go back to doing catering jobs "because I didn't have any money". Harden debuted on Broadway in the role of Harper Pitt (and others) in Tony Kushner's Angels in America in 1993.