It would have to be challenged in court.
Realistically, how can anyone prevent someone from running for president, based on him or her not being a natural born citizen? Realistically, election officials in states are not going to remove such people from the ballot. Realistically, election officials would be sued, if they tried to do so.
Heck, this erudite group of principled conservatives on Free Republic, can’t agree on the definition of natural born citizen. Do we really expect various state and local election officials, to make such a determination?
Then that leaves the courts, and federal court cases, as the place where this issue can be settled. Then you have to decide, who will decide to file a lawsuit, against a specific presidential candidate, and/or political party, to get this issue into court?
The Supreme Court doesn’t just sit around and issue opinions on something, unless someone has filed a lawsuit on the subject. And even there, it’s likely a lower federal court will have to hear such a case, before it gets to the Supreme Court for final resolution.