Down here they're referred to as "Undocumented Workers".
Hmm, down here they're usually referred to as "Jose", "Juan", or maybe "Juanita". :)
Seriously, I'm a third-generation American on my maternal side (Paternal is pre-Revolutionary War), and my wife is a naturalized American citizen. There is NO ONE who is more sympathetic to the plight of economic migrant (mostly Mexican's) who've come to America, than I am.
That said (side issue), my industry has been all but destroyed by cheap foreign (largely Indian) labor. My country needs to defend our nation against a deliberate economic strategy by foreign nations like India to dump labor and steal the core of the IT industry. Immigration needs to be controlled.
Second, Mexican government officials and certain Californian Democrats are talking about the USA Southwest as some sort of American "West Bank", i.e. that the return of this territory to Mexican control is all but pre-ordained. I seriously believe that Mexico is encouraging emigration to the USA as both a "re-conquistadora" strategy as well as an economic relief valve, and I'm just not willing to cede my children's birthright to foreign nationals with no allegiance to my country. Our borders need to be secured.
I'm very much concerned that a large number of immigrants entering the USA in a digital age that does not require sacrifice or divorce from their homeland of origin will result in a huge number of legalized resident aliens or new citizens who have no stake in our nation's security. I don't want my country to be a "New Mexicana", a "New India", an Islamic Caliphate, etc., nor do I want 400 years of American traditions which made the USA different from every other country supplanted by foreign cultures. I can never be Mexican, Indian, Japanese, or European. The USA is the last stop for my family, and we're won't move over or move out for someone else.