gives a good summary of why Trump can't do this (sorry, it's a reddit link). In short, jus soli is granted by the 14th amendment in no uncertain terms, and executive orders don't alter the constitution.
I will have to respectfully disagree with your position on the sentiment of Trump's statements. In my opinion, immigration is far down the list of problems that we should be addressing. Point of my last post was to be a reminder that the USA is unequivocally a nation of immigrants, and the actions Trump and GOP are taking (or trying to take) erode our claims of being "the land of the free."