It would be interesting to see what at short term lowering of immigration would have on wage growth.
Personally, I have nothing at all against the illegal sort. Day laborers, for instance, tend to be great workers and good people, happy to put in a hard day's work for a $50 and some good meals. At the same time though, I have to consider that this is really distorting the economy since it drags down wages for all people willing to do this work to that level, which is not really fair to people that want to make a living doing this work but want a higher standard of living, to raise a family, etc.
On the lowest rung of society, they're at least 50%. The higher you go the lower the percentage, and it drops off pretty fast.
I don't have exact figures so I'm using 50% like "about half". I suspect though that it's only about half because some of them managed to legalize themselves, and in reality in these very bad jobs there's actually even more than that.