Ummm - were you reading the dissent or the judgment? The Wong Kim Ark case declared that the child of Chinese immigrant laborers was a U.S. citizen (explicitly overruling the Slaughterhouse cases). Or did I miss something? (The dissent occupies the bottom third of the webpage).
Nope, you are correct, the Supreme Court did in fact rule in favor of the Chinese man born in the US. But his parents were legally present at the time of his birth. What I'm referring to are those of illegal aliens, of which the court has not ruled on as of yet.
Section 5 of the 14th Amendment reads:
The Congress shall have power to enforce, by appropriate legislation, the provisions of this article.
They will have to write into legislation first illegals and their offspring are not subject to US jurisdiction, at which point it will then be tested for its Constitutionality. I believe the current Supreme Court will uphold it.