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I wouldn't attribute the American left to Nazism, though it's hardly worth arguing about, the suppression of the masses motive is the same. But the American left predates Hitler. The impact of the American left, particularly on issues of race, had a major impact on a certain Austrian corporal. That should be ignored.
Edward Bellamy wrote one of the best selling books of its day (1888), entitled "Looking Backward" a Socialist utopian work of fiction. It was the third best selling fiction book in the USA during the 19th century, behind Uncle Tom's Cabin and Ben Hur. He coined the term "Nationalist" to rebrand the term "Socialist" as he felt it would be more easily accepted by the public.
The Nazis (i.e. Nationalist Socialists) adopted not only that as the primary term for their ideology, but also the stiff-armed salutes used by the Nationalist Clubs of Bellamy's followers (which later merged into the People's Party, which itself merged into the Democratic Party, getting the Vice President slot from the Democrats in 1896). These were not just a few cosmetic similarities, but rather a continuation of the whole political movement, grafted onto German national/ethnic themes and mythology.
The decades of work performed by the USA's Democrat Party in the American South crafting laws to enshrine racial segregation, as well as the Federal bureaucratic segregation instituted by the Wilson Administration, were consciously lifted whole cloth by the Nazis to institue their racial policies.
The eugenics programs of the Nazis were built on (probably inspired by) those of American "Progressives", like Margaret Sanger, founder of Planned Parenthood, and Leftist Brits like John Maynard Keynes, Director of the British Eugenics Society (right up until 1944). Many prominent Democrats like Joe Kennedy (then Ambassador to England) openly approved of the Nazi political platform, and the Democrat Party supporting Time Magazine named Herr Hitler its Man of the Year for 1938. FDR was enamored of Giovanni Gentile (the "Philosopher of Facism", Mussolini's Philosopher") and distributed Gentile's book to his cabinet. The Nazis were actually not that much of an innovation at all in the political spectrum, but their roots among their forerunners in America (now the Democratic Party) have been firmly pushed down the memory hole by Leftist teacher's unions and the media. They now pretend they were ideologically the opposite of the Nazis. What Chutzpah.
1890's American "Nationalist" socialists: