Dempsey in 1932 was appointed a member and later president of the Board of Regents of the University of New Mexico. He served as the state director for the National Recovery Administration in 1933, then became state director of the Federal Housing Administration and the National Emergency Council. He was elected as a Democrat to the Seventy-fourth, Seventy-fifth, and Seventy-sixth Congresses (January 3, 1935-January 3, 1941) but was not a candidate for renomination in 1940 when he was an unsuccessful candidate for nomination for United States Senator.
Dempsey served as a member of the United States Maritime Commission 1941. He was the Under Secretary of the Interior from July 7, 1941, until his resignation on June 24, 1942. He was Governor of New Mexico from January 1, 1943, to January 1, 1947 and was unsuccessful candidate for the Democratic nomination for United States Senator in 1946. 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. He was buried in Rosario Cemetery, Santa Fe, New Mexico.