1. If I were living in Mexico, and saw that I could provide better for my family by sneaking into the U.S., I'd probably do it.
2. Everyone knows that they come here because people hire them. If people didn't hire them, they wouldn't be here.
3. Just as it's illegal to be here without permission, it's illegal to hire someone who is here without permission.
Given those three premises, I don't think it's fair to target enforcement exclusively on the immigrants. I think it's unconscionable to conflate this issue with terrorism, as I keep hearing.[1]
There is a perfectly reasonable compromise, that no one should be able to agrue with: Do enforcement sweeps at businesses suspected to be employeeing illegal immigrants. If any are found, deport the immigrants and arrest the employer. I say this is a compromise only because it throws a bone to the "kick them out" crowd. If you only arrested the employers, the immigration would stop on its own once the jobs dried up.
[1] Heard on the radio today: "Either we're engaged in a worldwide war on terror or we're not. If we are, then we must secure our borders. That is the only question here."