Now that the Senate has killed the Immigration Bill (at least temporarily), I'd like to address this. I am convinced that we are going about the effort to stop illegal immigration the wrong way. Enforcement plans always seem to focus on the illegal immigrants. From an economic standpoint, in the Supply and Demand model, the immigrants are the Supply. They are the cheap labor that employers (mainly agricultural, restaurant, and hotel if you believe the anecdotal claims) hire because, supposedly, Americans don't want those jobs. These employers represent the Demand portion of the economic equation.
We should have learned from years of failed enforcement efforts that stemming the tide of the supply of illegal immigrant workers is impossible. For every illegal we catch and send back home, dozens replace him. We can't stop or even realistically slow down the supply pipeline unless we build a concrete wall between the entirety of the border with Mexico.
In order to win this battle, if it can be won, we must go after the Demand side of the equation rather than the Supply side. If there are no jobs to be had for illegal immigrants, much of the impetus for their coming is removed.
So, if we really want to stop or greatly reduce illegal immigration, the solution is to enforce stiff penalties against employers who hire illegal immigrants. Make it hurt. Heavy fines for first offenses. Subsequent offenses should include jail time. If we really care about this issue, this is the only way to solve it.