That would be okay--to have an unofficial immigration standard that results from the push and pull between opposing views about the enforcement of the official standard--if not for the fact that illegal immigrants are shut out from so much of American society. Severely limited employment opportunity is the worst part, I imagine, but there is so much more than that. Fear of deportation excludes illegal immigrants from all sorts of rights and privileges to which the rest of us have access. For example, if I have cause to sue someone, I wouldn't generally fear any repercussions from filing a lawsuit. But I would not want to enter into any kind of legal proceeding if I faced a risk of my immigration status being discovered. Even if we disregard explicit threats ("If you don't do ____, I'll call the INS"), there are countless situations in which an illegal immigrant would have to accept something that would be unacceptable to a citizen.
Amnesty is not just about letting them stay. It's also about letting them exist like everyone else.
BTW, what image springs to mind when you hear the phrase "illegal immigrant"? For me it's someone working hard to eke out a decent existence for himself and his family. Not someone we should turn away or turn into a second-class citizen.