I cannot speak to the south side, specifically, but how many Illini fans should we expect?? The Chicago Area is fundamentally a different beast to Milwaukee for Wisconsin or Cleveland for Ohio State or even Detroit for Michigan/MSU. There will always be too large of a population and too many transplants for the Illini to dominate the market like we could a smaller, less nationally relevant city. That's just the way it is, for better and for worse! Our instate support in Central Illinois is just as good overall as any other Big Ten school's in their state (with the possible exceptions of truly psychotic instate loyalty for Nebraska and Iowa), and I think our support in Downstate Illinois as a whole is quite good. Our support in Chicagoland has a relatively high floor, but it really explodes when we are good, from my experience. Sucks to admit it, but we have a lot of fair weather Illini fans in Chicago, which is unfortunate most of the time but also gives our program a high ceiling as far as TV ratings and fan following if we get things going (e.g., Chicago responding super well to the Rose Bowl season).
With that said (and again acknowledging that I cannot speak to the south side), I have always found the Notre Dame presence in Chicago incredibly exaggerated. Sure, they have a lot of fans (probably fourth most prevalent up here in the Roscoe Village area after Illinois, Michigan and likely Iowa), but they are FAR from some type of "home team" in the broader Chicago Area, and there are easily more Illini fans overall, even if they're quieter. The Tribune actually just recently did a poll of all of its readers, and Illinois had 30% support, with Notre Dame at like 19%.
EDIT: However, yes, if we are talking about our sway with Chicagoland high school football talent ... we have been punching WAY below our weight for far too long.