They are here because the Gov't has failed to protect our borders. They aren't going away because law enforcement and the INS are not doing their jobs. They have all but given up. When law enforcement agencies take the Mexican ID card rather than turning illegals over to the INS for deportation no, "they aren't going away".
We need to enforce the laws on the books. Prosecute employers who hire illegals, deport illegals anytime they are caught, and protect our borders so they don't get in to start with.
I, like you, agree with immigration, but not with illegal immigration. The Center for Immigration Studies estimates that each illegal takes $55K more from the system than they contribute over a lifetime. This is appalling. We need controlled, legal immigration with a means testing.