Until fairly recently labor was bending over backwards to enforce such controls in the belief that such laws were effective protections for American workers. The union movement is historically skeptical of markets and its adherents mostly subscribe uncritically to the 'lump of labor' fallacy. It's only in the last few years that they have jumped on the bandwagon for immigration reform; prior to that they were happy to blame a lot of their own structural problems on an influx of Mexicans.