Maw was elected to the Utah State Senate in 1928 where he served until 1938. Maw served as the President of the Utah State Senate from 1934 until 1938. He was an unsuccessful candidate for the Democratic nomination for the US Senate in 1934 and Governor in 1936. His loss was partly a result of his strong support of measures to help workers. Maw's winning the Democratic nomination in 1940 was largely the result of his successful push for direct primaries.