Dr. John Fonte, Senior Fellow of The Hudson Institute had this to say about the issue at a Congressional hearing on dual citizenship from September 29, 2005: Dual Citizenship, Birthright Citizenship, and the Meaning of Sovereignty
The authors in the legislative history, the authors of that language, Senator Lyman Trumbull said, ”When we talk about ’subject to the jurisdiction of the United States,’ it means complete jurisdiction, not owing allegiance to anybody else.” Senator Jacob Howard said that it’s ”a full and complete jurisdiction.”
This illustrates that Congress recently discussed the issue, and they can’t claim they were unaware. But we don’t have to take Dr. Fonte’s word for it. The following discussion by the various 14th Amendment Framers took place on the Senate floor. I took it from P.A. Madison’s research at The 14th Amendment to the United States Constitution - Fourteenth Amendment - anchor babies and birthright citizenship - interpretations and misinterpretations - US Constitution (use his link for footnotes):
It is clear the framers of the Fourteenth Amendment had no intention of freely giving away American citizenship to just anyone simply because they may have been born on American soil. Again, we are fortunate enough to have on the record the highest authority tell us, Sen. Lyman Trumbull, Chairman of the Judiciary Committee… and the one who inserted the phrase:
[T]he provision is, that ‘all persons born in the United States, and subject to the jurisdiction thereof, are citizens.’ That means ’subject to the complete jurisdiction thereof.’ What do we mean by ‘complete jurisdiction thereof?’ Not owing allegiance to anybody else. That is what it means.