The 14th Amendment States:
“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.”
The argument will be on the phrase: “and subject to the jurisdiction thereof”.
So my guess is that an EO need merely to declare a judicial-esque interpretation of what this phrase means... something that SCOTUS can then validate... and declare this interpretation to be the policy of the United States for implementation of the 14th amendment's provisions.
That said, it will be important to have a SCOTUS decision so that any future administration would not be able to rescind this coming EO.