We have a guest worker system --- green cards, several programs for guest workers --- not everyone chooses to fill out forms or wait in line. There will be those that figure it's easier to break the law than to follow it --- adding more and more guest worker programs won't solve the problem.
Of course the other solution is don't allow any guest workers and force people who are physically able off the welfare rolls and put them in those jobs. I for one would love to see that, but these people wouldn't work. But then again if the didn't, let them starve and cut off the source of money for their lottery tickets and crack cocanine.