I don't think anybody is "for" illegal immigration, in the sense of "oh boy, let's have lots more illegal immigration". If no no other reason than it's chaotic. It's much better to have an orderly influx.
This is not to say that there aren't people who think our posture toward Latin America is too restrictive, or too harsh, or too long a process to get in, or too low of a quota, or too whatever. But that's a desire to change the legal structure of immigration, which is a very different thing from cheering on illegals. No, the bone of contention is what to do with them now that they are here. It's clear that not allowing them to work hasn't been effective, because they are still here and, since they can't work, they are feeding their families any way they can. So now the complaint is they are a drain on the system. SO LET THEM WORK. Hell, REQUIRE THEM TO WORK. We require Americans on welfare to get jobs, why do we have undocumented receiving assistance but not being allowed to work? It makes no sense.
If they pay taxes and are actively trying to gain citizenship im cool...but cross the border legally so we know who you are and how many Non citizens we have.