It's not a great case, which is why many Rs are talking constitutional amendment. "All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the state wherein they reside." So you hang your hat on what "subject to the jurisdiction thereof" means. Best case law against is maybe the Slaughter-House cases, but that was about children of diplomats of foreign countries. Elk v. Wilkens was about Native Americans, which was overturned by statute and not applicable b/c they were subject to their tribes, which had things like the power to enter into treaties, etc... that don't apply here. There is no SCOTUS case on whether it applies to children of illegal immigrants, but whenever you get into drafters' intent, it's messy. Upholding birthright citizenship would be Kagan, Breyer, Ginsberg, Sotomayor, likely Kennedy (I'd put him at ~85% based on his Boumediene stuff), likely Roberts (~65%?). Opposing you might get Scalia (his discussions on founders' intent are... selectively chosen, I'd say), Thomas (likely), Alito (no idea). It would be interesting, but I don't think most conservatives are keen to push it (also have to repeal a statute, but that's easier).
The problem with intent is that it's extremely messy. Do you credit statements from the main proponent (but he's just 1 vote)? Committee notes? The amendment process (w/out getting into detail, it's very easy, and somewhat common, for adopted laws to include things that no one really wants). How do you weight competing interpretations? Signing statements? Statements to newspapers count the same as statements on the floor? Most blowhard/talkative Senator count for more? That's why textualists have discarded intent in favor of, well, textualism for statutes (Scalia was the big proponent of this before he was on the Supreme Court, let alone now). That they tend to be the most vocal intent proponents for anything Constitutional is interesting, to say the least.
