The U.S. labor movement was never really explicitly socialist, and certainly not the one that existed during the passage of the New Deal,
many of the organizers of the 1930s, especially with the CIO, were socialists, and during the Comintern's 'popular front' period many people who were deeply involved with the CPUSA worked within organized labor. I can point you to an Irving Howe essay if you actually care. you could also read up on the 1934 strikes in Minneapolis, a heroic and bloody effort led by avowed Trotskyists that ended in the unionization of the trucking industry.