The bottom line is that we need the workers to do all the jobs Americans distain. I believe that's why the problem has never been solved.
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I believe a far simpler solution would be to arrest and confiscate the property of employers who hire illegals. Make the practice a felony. Give them one shot to sign up their illegals into your proposed guest worker program.
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As noted most illegals are poor. They come to "the land of opportunity to find work." If you remove the incentive, illegals will sign up for the Guest Worker Program or leave.
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The problem is that politicians will not admit that all these workers are needed, because then the voters scream, "They are taking our jobs." I did not send my kids to college to pick crops in the fields, clean toilets, make beds, or mow lawns.
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It's a much better political football than a problem to be solved.