Ted: I acknowledge your point about "waiting your turn in line." It is a distinctly American value grounded in the notion that everyone here is (or at least is supposed to be) equal, and have equal rights. Viewed in isolation, that argument is a compelling one for limiting immigration to legal immigration.
I would note, however, that, for most of these immigrants, waiting in line for a work visa or other legal permission to enter the U.S. is hardly comparable to waiting in line for entrance to a movie theater, amusement park ride, etc. Most of them are impoverished, many are malnourished, and many of them are escaping a country of origin where their personal safety was at considerable risk. Under those circumstances, the average person is likely to be a bit less concerned about patiently waiting his or her turn in line. Particularly if it means months or years of waiting.
Finally, this illegal immigration occurs ONLY because there are job opportunities here in the U.S. for illegal immigrants. Illegal; immigrant labor has LONG been a feature of the U.S. economy, so the blame (if you wanna call it that) for illegal immigration hardly falls at the feet of immigrants alone.