Major,
You need a hybrid. I'm all for deporting illegal immigrants and securing the border. However, that's not enough. In fact, by itself, it's almost meaningless, because the incentive to come is far too great. They're always going to try, and some will get through.
You are correct that it's not the employer's job to control, prevent or police immigration. He has no control over that. However, he does have control over who he hires. It's just as illegal for him to hire the illegal alien is it is illegal for the illegal alien to be in the country.
I'm all for deporting the illegal alien. However, while you're at it, fine his employer (who's as big of a lawbreaker as he is) $1,000.00 per day he's on the job, per illegal immigrant, and the problem will go away. He'll think twice before breaking the law to save an extra $7/hour.