Asinine suggestion.
How about this instead.
We have a Green Card / Red Card system.
The Green Cards work similar to the way they do now with residency and work requirements, and with whatever social services the State of residency provides for them.
The Red Cards are 3 month work permits that require an assurance from an employer. Red Cards are same day issue, but are subject to a fingerprint match. (That's right, fingerprint every foreign entrant!) Red Cards can be denied by accumulating 10 points in the Immigration Services database. These points can be reviewed once every year upon appeal. Typical actions that would cause points to be "awarded":
-Violent felony 10pts
-Possession or distribution of false immigration documents 10pts
-Entering the United States at a point other than an Official Checkpoint 10pts
-Failure to renew your Red Card 5pts
-Criminal Misdemeanor 1 to 5pts
If this were to go into effect, then you could aggressively start patrolling the border without fear of harming immigrants who just wish to work. Since everyone could enter and work (and pay taxes) as long as they hadn't broken the rules in the past, only those with something to hide about their nature would be trying to slip across unnoticed.
I realize that this is just a brief sketch of an idea that I have been working on, but I believe you can see that it would provide a way for Mexicans in particular to improve their lives while still providing the U.S. with a secure border and keeping us from losing tax revenue from under the table payments. Will it magically solve all the problems? No, I have no illusions that it would. But I do think it would be a big step in the right direction.
Maybe even save a few people from dying in the desert while reaching for the American Dream.