Those poor people of right now generally are not competing with illegal immigrants for jobs. They do jobs that americans do not want to do, and they bust their asses doing them for not enough money.
I have repeatedly advised a system of very cheap visas for people who want to come to america to work. They would then be verified, since we would have their information. They wouldn't be illegal, we have their information, they're in a better position to push for better pay and be treated like actual human beings. Where's the downside?