Employed as a telegrapher, he held various positions with the Brooklyn Union Elevator Company.

He was the vice president of the Brooklyn Rapid Transit Company until 1919 when he entered the oil business in Oklahoma and became vice president of the Continental Oil and Asphalt Company.

He moved to Santa Fe, New Mexico, in 1920 and was an independent oil operator and in 1928 became president of the United States Asphalt Company.

Dempsey in 1932 was appointed a member and later president of the Board of Regents of the University of New Mexico.

He was elected to the Eighty-second and the three succeeding Congresses and served from January 3, 1951, until his death in Washington, D.C., March 11, 1958.