It's too left-wing for most Democrats to talk about, too.
Actually, that's not how the WPA was seen at the time. The American Federation of Labor (that bastion of conservative, business-oriented trade unionism) as well as the Communist Party, the Socialist Party, etc. all condemned the CCC and the WPA as 'forced labor programs', iirc around the time that they were enacted. The 'left-wing' solution to the Depression at that time was a reduction in working hours, which was proposed as early as 1933 by folks like Hugo Black, who introduced an amendment to the National Industrial Recovery Act to establish a 30 hour workweek (which was uniformly backed by the left; it didn't see the light of day because the Roosevelt administration strongly opposed such an amendment, favoring instead to create make-work programs.) Indeed, it's kind of weird that
creating wage labor is now seen as the
left-wing solution to our current woes, given that left-wingers prior to the 1930s would have been wholly opposed to such 'solutions' because they were much more favorable to plans aimed at shortening the amount of time people spent under wage labor, rather than increasing the overall amount of people forced into it.