Funny. I read the phrase through the intent of the Amendment's sponsors and THEY also excluded foreigners and aliens.
I will again link to this article by P.A. Madison. I am not linking to it as endorsement of him (I don't know him) but he has put together a very good synopsis of the Congressional arguments made at the time of the Amendment's adoption. You can argue with them...
I read Mr. Madison's article. I found it wanting, both factually and in its conclusion.
First, despite the intent of Howard, there were PLENTY of voices that were heard during debate on the proposed amendment from legislators that knew full-well what the practical consequences of such an amendment would be. There's a book called The Fourteenth Amendment: from political principle to judicial doctrine that nicely fleshes out the debate leading up to the ratification of the amendment. In the book, many Senators and Congressman are quoted lamenting the fact that the Amendment would give birthright citizenship to everyone and anyone (save for children of diplomats and invading armies), who was born in the country. You can see some of this recounted in the book here. One Senator (I believe from Pennsylvania) rails that the Amendment would give citizenship to the children of "trespassers and gypsies". He was right.
Moreover, Madison misses completely the relevant case law. And, you cannot have a discussion of constitutionality, absent the relevant case law. He says in his concluding paragraph...
In a nutshell, it means this: The constitution of the United States does not grant citizenship at birth to just anyone who happens to be born within American borders. It is the allegiance (complete jurisdiction) of the child's birth parents at the time of birth that determines the child's citizenship--not geographical location
This completely ignores United States v. Wong Kim Ark, 169 U.S. 649 (1898). In that case, Gray in writing for the majority, says this about Ark...
The evident intention, and the necessary effect, of the submission of this case to the decision of the court upon the facts agreed by the parties were to present for determination the single question stated at the beginning of this opinion, namely, whether a child born in the United States, of parent of Chinese descent, who, at the time of his birth, are subjects of the Emperor of China, but have a permanent domicil and residence in the United States, and are there carrying on business, and are not employed in any diplomatic or official capacity under the Emperor of China, becomes at the time of his birth a citizen of the United States. For the reasons above stated, this court is of opinion that the question must be answered in the affirmative.Order affirmed.
emphasis added
I suppose Mr. Madison is entitled to his opinion, but his opinion is CLEARLY wrong, as is demonstrated by the central legal holding in Ark.