As long as we have a wealthy, Information Age superpower with a need for unskilled labor next to an impoverished, corrupt, mismanaged Third World nation, we are going to have immigration from the latter to the former. And if you think it's bad now, wait until the production at Canterell declines for another couple years and Mexico has to import oil. Remember how lousy the U.S. economy was in the Seventies? That was caused in large part by U.S. oil production peaking and us suddenly having to import more oil, worsening the balance of trade.
We need to pressure Mexico to reform and improve its economy even as we build our border fence and clamp down on illegal immigrants...understanding there is no overnight cure for this. If we deport a couple million illegal immigrants, that's a couple million jobs that are going to go unfilled, creating an economic imbalance that is simply going to spur...you guessed it...more illegal immigration. Sure, some of those jobs would be filled by Americans...but not many. What would happen is a few jobs would be taken by Americans, and wages would go up.
Rising wages sounds like a good thing. Economics is funny about that sort of thing...there's always at least a catch, and usually more than one. Higher wages for unskilled labor would drive up the cost of producing goods and services, leading to higher prices for everything from cheeseburgers to a month's rent. Higher wages would also increase the incentive for illegal immigration. And, over the long run, higher wages for unskilled labor encourages firms to make do with fewer employees, reducing employment over time.