Abe Murdock was a staunch Democrat from his youth and he worked his way up the political ladder by holding a number of political offices. He was elected as a member of the Beaver city council in 1920-21. He served as Beaver County Attorney for three terms (1923-24, 1927-28, 1931-33). He also served as Beaver City Attorney from 1926 to 1933.
Murdock was elected to Congress from the First District of Utah in the Democratic sweep of 1932. He was elected four times to Congress and served from 4 March 1933 to 3 January 1941. In 1940 he was elected to the U.S. Senate after defeating former senator William H. King in the Democratic primary. Murdock served only one term, as he was defeated for reelection in 1946 by Arthur Watkins.
During his political career Murdock was known as a strong supporter of President Franklin D. Roosevelt's New Deal policies and as a solid backer of organized labor. Murdock served on the House Judiciary Committee and on the Senate Banking and Currency Committee. He was also active in supporting water reclamation projects in Utah. Murdock was active in Democratic party affairs and served as chairman of the credentials committee of the 1944 Democratic national convention in Chicago.
Murdock was appointed to the National Labor Relations Board (NLRB) by President Harry S Truman in 1947. He served two consecutive five-year terms, and upon his retirement in 1957 Murdock was hailed as one of the "giants in NLRB history." Murdock stayed in Washington, D.C., upon his retirement. He was appointed a member of the Atomic Energy Labor-Management Relations Panel for a short time in 1960. He died of natural causes in Bethesda, Maryland, on 15 September 1979 and is buried in Mountain View Cemetery in Beaver, Utah.