I think it refers to the ordinary working man; thus:

Charley said that working stiffs ought to stick together for decent living conditions.
- John Dos Passos, _42nd Parallel_, 1930

The idea of two young working stiffs [Woodward and Bernstein] carrying off the prize is irresistible to youngsters with their careers before them. - Guardian Weekly 10 July 1977

(Dos Passos is the earliest cite in OED2)

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then there is "working stiff" as used in pro wrasslin', which means pulling no punches, in a style that could actually hurt your opponent (and/or yourself!).