Born in Kayville, Saskatchewan, he was first elected to Parliament in 1945 representing the Co-operative Commonwealth Federation (CCF). When the party nearly was wiped out in the Diefenbaker sweep of 1958, Argue became House Leader, and was elected national leader of the CCF at the party's convention on August 11 1960.
Despite Argue's opposition, a number of leading figures in the CCF, attempting to develop a strategy to rebuild the party, came to advocate relaunching the party on the model of the British Labour Party by creating a formal alliance between the party and the Canadian Labour Congress.
In 1961, Walter Pitman won a stunning by-election victory in Peterborough under the name "New Party". "New Party" clubs sprung up around the country and the CCF, New Party Clubs and the CLC, combined to launch the New Democratic Party. Argue was a candidate at the first leadership convention against long-time Saskatchewan Premier Tommy Douglas. During his speech to the convention, Argue promised:
"No matter my role, I give you this pledge; that in the years ahead, I shall speak for you, I shall work for you, I shall never let you down" Argue was defeated resoundedly winning only 380 votes against Douglas' 1,391 votes. Hurt by this rejection, Argue crossed the floor six months later to join the Liberal Party arguing that divisions were rife in the NDP and that farmers' interests were overwhelmed by those of labour. He was re-elected as a Liberal Member of Parliament (MP) in 1962 but was defeated in 1963 and again in 1965.
In 1966, Argue was appointed to the Senate as a Liberal.
When the Liberal Party failed to win any seats in the House of Commons from ridings west of Winnipeg in the 1980 election, Argue was appointed to Pierre Trudeau's Cabinet from 1980 to 1984 as Minister of State (Canada Wheat Board).
Senator Argue faced disgrace in 1988 when criminal charges of fraud were filed against him when it was alleged that he had misused Senate supplies and services but he died before the case came to court. In 1989 he was criticised for promoting a psychic surgeon visiting Regina as a legitimate medical practitioner.
Argue is the only former leader of the CCF or NDP whose portrait is not on the walls of NDP headquarters.