Maybe you are thinking of the character (Julia) she played in Designing Women.
Are you sure y'all aren't thinking of Delta Burke? She was shredded by the media for gaining weight while on the show, but I believe she and her husband, Gerald McRainey, are Rebpublicans.
Yes, you are right. Delta Burke and her husband are republicans but believe me, so is Dixie Carter. Dixie's character on Designing Women was very liberal. I heard her say in an interview that she was nothing like her character. She said that she has always been a conservative.