That's not inherently the implication of that study. Other valid implications include: Work goes undone, full-time hires are being exchanged for part-time hires, cash flow becomes strained in firms that can neither replace workers with part-timers or reduce their hours.
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Certainly. I would say that a non-zero number of reasonable people consider the GOP anti-amnesty because illegal immigrants are easier to control as a workforce, and that the GOP kowtows to their corporate masters. The Dems do as well, but the types of immigrants don't tend to intersect.