I don't know why a person who was born here deserves more opportunities than someone who wasn't. If we're gung-ho about any kind of capitalism (I'm not, obviously but that's another conversation), then it makes sense to support more competition at all levels of the economy. And if you have population growth, the demand for workers will also be affected as new businesses and enterprises come into being.
I do agree that if you care about illegal immigration, what needs to be done is a serious check on the capacity of companies to hire illegal aliens. That's a primary driver of the influx.
From my position, I want to see 0 illegal immigration and a points system like Canada and Australia have. A personal who is an illegal immigrant who has cut the line for economic gain should be deported. They are taking resources from people here legally. Essentially there are only so many resources - so yes, the person here legally (born here, legit asylum seeker, legit refugee, legal immigrant) is more deserving. They didn't break any laws or think the rules don't apply to them.