In 1991 she married Brad Thompson, a former bus driver for Clint Black, but the two divorced in 1993. During her marriage to Thompson, she suffered from ovarian cysts which led to a hysterectomy. Morgan began dating American football player Troy Aikman in late 1993, but they amicably separated by year's end. From 1994 to 1996, Morgan was romantically linked to actor and politician Fred Thompson. Morgan observed that her relationship with Thompson increased her personal interest in political matters, but also caused her to "stop and think about the political implications of everything before I uttered a word in public." She also observed that she wished to marry Thompson, but felt that his political background would keep him from accepting her for who she was.