I know that is how the law is currently applied, but would it take a constitutional amendment to change that? The 14th amendment says:
"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"
Could the words "and subject to the jurisdiction thereof" be used to exclude people born to non-US parents? Apparently Native Americans were not citizens until 1924, long after the amendment.
If Congress were to pass a bill denying citizenship to children of non-US parentage do you think it would stand the legal test?