In 1962, Whittenburg lost the Republican gubernatorial primary to Jack M. Cox, then an oilfield equipment executive from Houston, who was in turn defeated in the general election by the then Democrat John B. Connally, Junior. Whittenburg said that he wanted to be governor to check the "dictatorial powers" of United States. President John F. Kennedy. Whittenburg was born in the ghost town of Plemons in Hutchinson County in the Texas Panhandle.
The couple had seven children: Grace Evelyn Coltrin (born 1939), Jewel Anne Johnston (born 1942), George Allen Whittenburg (born 1944), Louis Palma McKee "Mack" Whittenburg (born 1946), John Burkhart "Burk" Whittenburg (born 1948), Mary Lois Rowley (born 1955), and Roy Whittenburg, Junior.
(born 1958). The Whittenburgs are interred at Dreamland Cemetery in Canyon in Randall County, where Roy Whittenburg resided at the time of his death at the age of sixty-seven.