After school he was apprenticed to a stonemason. He became active in state and federal branches of the Operative Stonemasons’ Society of Australia and in 1938 was employed on the project to complete Parliament House in Adelaide. He used to joke that as he had worked on parliament there was every reason why he should work in parliament. In 1941 he was elected as ALP member for the House of Assembly seat of Goodwood, later renamed Edwardstown, and held that seat until he retired in 1968. In 1949 he was elected deputy leader of the parliamentary Labor Party and in 1960 its leader.

Walsh was a typical old-style Labor politician from a union background. He believed in looking after workers’ interests and in expanding industrialisation rather than in social reform. His speeches were in the rhetorical tub-thumping style which did not suit the new medium of television. As a Catholic, he had no patience with those who wanted to bring religion into political matters, but he demonstrated his Catholicism in practical ways: by assistance to the Carmelite nuns (for whom he built a pottery kiln), the Good Shepherd Sisters and the Little Sisters of the Poor. He did not approve of Don Dunstan whose background, political interests and style were so different from his own. In 1965 the seemingly eternal Playford government was defeated and Walsh became the first Labor premier of South Australia in 32 years. He was also the first Catholic premier. Aged 67 when he achieved office, he was obviously a stop-gap leader. However, he did initiate gambling law reform, which led to the establishment of the state lottery and the TAB, and he obtained Commonwealth assistance to build the natural gas pipeline from Moomba to Adelaide. Rather against his wishes, on reaching the retiring age laid down by party rules, in June 1967 he stepped down as premier to be succeeded by Dunstan, but he remained minister for social welfare until the next election in 1968. He died a few months later and was given a state funeral at the cathedral where he and his wife Hilda had regularly attended Mass.