Should babies of illegals be granted U.S. citizenship just for being born within U.S. borders?

Our immigration system, to me, seems to reward illegal activity while discouraging actually skilled people to stay. For instance, illegals who sneak across the border to give birth (for free to them) have a child that is granted U.S. citizenship. On the other hand, we quickly deport international college students because their student visas expire quickly after school is over. Thus, we end up with an immigration problem of masses of unskilled workers who now need to live off of a system that they never paid into. Anyways, what do you guys think? Should we automatically grant citizenship for simply being born within U.S. borders?