If you look at states like Georgia (and i've seen similar articles about parts of the UK), there's a massive shortage of farm workers, and regardless of what the supply of illegal migrant workers is. Even after Georgia began holding farmers directly liable for employing illegal immigrants, local workers have not stepped up to fill the gap.
Besides, American immigration policy, rightly, allows white collar workers from other nations, especially Canada and Mexico into the country via NAFTA. That is, frankly, a good thing. All we're doing is keeping out a labor supply that is currently needed.
If you want to level the playing field for native low skill workers, require farmers and the like to pay all the taxes and health benefits for all their workers, illegal or not.