He is James (Chip) Carter III's son. James III was born in 1950 and James IV was born in 1977. Amy was born long after the three boys who were on there own by the time Jimmy was elected.
http://www.georgiaencyclopedia.org/nge/Article.jsp?id=h-2735
Hmmmmm I wonder if ol' Jimmah was feeling more than just lust in his heart when he gave that Playboy interview?