Perhaps the most left-wing candidate for President, but the most left-wing Vice President was certainly Henry Wallace, who wanted (among other things) nationalized health care.

“In 1946, Wallace publicly broke with President Truman over the issue of opposing Stalin’s bid for domination of Europe. Two years later Wallace ran as the liberals’ antiwar candidate. He opposed the Berlin airlift and blamed the fall of Czechoslovakia to the Communists on the United States. His campaign attracted many academics and intellectuals who saw him, not Truman, as the true champion of New Deal liberalism.

But the real backbone of his Progressive Citizens of America was the American Communist party. Its chairman was a secret Communist; John Abt, its general counsel, was a Soviet spy who was part of the same Communist cell as Alger Hiss (Hiss himself worked for Wallace when he had been secretary of agriculture). The campaign’s platform committee was headed by another secret Communist, Lee Pressman. Every aspect of the official platform faithfully reflected the Stalinist party line. ”

http://www.nationalreview.com/comment/comment-herman121802.asp