Following his position as assistant counsel with Southern Counties Gas Co., from 1952 to 1956, Dutton became chief assistant attorney general of California, in 1957 and 1958. He was executive secretary to
California Governor Pat Brown in 1959 and 1960. Governor Brown appointed Dutton to the
Regents of the University of California in 1962, where he served until 1978. Dutton was the deputy national chairman of Citizens for Kennedy-Johnson in
1960. Following the election, he was brought into the
White House as a Special Assistant to
United States President John F. Kennedy in 1961, serving as secretary of the cabinet and special assistant for intergovernmental and interdepartmental relations. He was appointed
Assistant Secretary of State for Congressional Relations, from 1961 to 1964. He was also a political adviser and campaign aide to
Robert F. Kennedy. Dutton was asked to co-ordinate the John F. Kennedy Presidential Library, and oversaw its Oral History Project. Dutton travelled with Kennedy during much of his
1968 presidential campaign from his
1968 presidential election. He was at the
Ambassador Hotel in
Los Angeles, California when the
Senator was shot at the kitchen hotel, and rode in the ambulance with him at
Good Samaritan Hospital. Kennedy died the next day. In an interview after he became a lobbyist, he said "After Bobby was shot, the lights went out for me." ==Legal and lobbying career==