I don't really know what the law does--there's a difference between "Police can harass anyone they feel like," which I don't think its quite the language in the bill, and that police do harass random people. Perhaps people should take a chill pill and see how many wrongful arrests there are and how many deportations occur and then trade off the costs and benefits.
I don't think there is much of a benefit to deporting illegal immigrants. The problem with immigration is that it isn't fair, and the bias brings more negative externalities (social fragmentation, two-language equilibrium). Toying at the margin, kicking a couple people out, won't help with either of those problems. Kicking out a Mexican doesn't mean an African can come.
And then there is this great point from the comments: "In fact, historically, the Mexicans being excoriated by them probably have a greater right to be there than any of the Caucasians, given that the territory was militarily annexed from the Mexicans by the whites. It was their territory first." I wonder how hard people think before they say things like that. Since only the Native Americans were there what rights should Spanish Mexicans or Black Mexicans have? Should your rights be weighted by how Native American you are--and what if you're Mayan, do you have a claim on North American territory? Also, shouldn't the Mexicans who got annexed have to pay the U.S. government for the benefits of being Americans? (If you doubt that there are benefits ask yourself "If I had a choice between being a random person born in California or in northern Mexico, which would I pick?")