(Nicknames in bold are used in "Axis of Evil" scene and thereafter by Bush)

Karl Rove, deputy chief of staff: "Boy Genius" and "Turd Blossom" ("Turd Blossom" is Texas slang for a flower which grows from a pile of cow dung.)
(http://en.wikipedia.org/wiki/Turd_Blossom)

Condoleezza Rice, secretary of state: "Guru"
(Rice took a leave of absence from Stanford University in July, 1999 to tutor George W. Bush in foreign policy and prepare him for the 2000 Presidential Campaign, hence his nickname for her -- "Guru."
(http://www.answers.com/topic/condoleezza-rice)

Colin Powell, ex-secretary of state: "Balloonfoot"
(origin unknown, but in trucker lexicon, a balloonfoot is a cautious, slower driver (Powell) as compared to a leadfoot (Rummy). The nickname is real, but the reason for it is still speculative. Paul O'Neill ("The Big O") references "Ballonfoot" as W's nickname for Powell in "The Price of Loyalty," Ron Suskind, page 160.

George Tenet, ex-CIA director: "Brother George"

Dick Cheney, vice president: "Vice" and "Big Time"

Vladimir Putin: "Pootie-Poot"

Former President Bush: "41" and "Poppy"

Barbara Bush: "No. 1"

First Lady Laura Bush: "Bushie" and "First"

Donald Rumsfeld, defense secretary: "Rummy"

(http://politicalhumor.about.com/od/bushquotes/a/bushnicknames.htm)