If you can't get keep people from getting in, how do you spot them once they're here? I work with a Mexican national (he's legal, though). Without knowing better, I wouldn't be able to tell that he's an immigrant while some other person is not, and I've lived my entire life, save for one year, on the border. You could, of course, try to document the legal people (with, I don't know, some sort of passport) and force every person that looks like they could be illegal to present identification. I know I for one would love to live in a place that unfairly persecutes anyone that isn't white! </sarcasm>
Get real, the only way to ease the problem with illegal immigration (and with borders the size of the US, you'll never get rid of it) is to make the process of becoming legal a sane experience. It takes something like 18 years just to have the chance to get into this country if they're from a Latin country. It's no wonder people would rather hop a fence.