If immigration laws were strictly enforced and employers were truly afraid of the consequences of getting caught hiring and employing illegal aliens, then most employers would stop hiring them. The jobs would no longer be available, for the most part, and illegal aliens would start going home on their own. They would self deport. A wall, fence, or other border barrier is critical to this to ensure that if our policies change again, they can't all come pouring across the border again.
You and the President offer two false choices. The choice is not only between deporting every one of them or offering them amnesty and rewards. There are other possible solutions. I can tell you that any form of amnesty, further rewards, or a privileged path to citizenship will only make the problem worse. History has proven this. And that is putting aside just how WRONG it is to reward lawbreakers.
I obviously don't agree with your punishing employers for hiring hard workers. Your assumption that they will head home may or may not come true if they can find any work whatsoever here. Most can make more money panhandling than they can make in Mejico.
I am not offering them rewards other than the opportunity to earn a living w/o any citizenship benefits. When you have full employment you need people to fill those jobs.
Pray for W and Our Freedom Fighters