In the fight between labor and capital, the favored class is right there on the label of the economic system. Class warfare is a built-in feature of capitalism - no mainstream American political party is going to repudiate capitalism; the DSA is far from the mainstream and this is exactly its main bone of contention with center/center-right liberals. There hasn't been an unabashedly pro-labor major political party in the US anymore since Bill Clinton's "Third way".