Aside from the fact that blacks, indians, etc that were born in the U.S. weren't even citizens until the 14th and later. Even under the 14th, those born in the United States to foreign nationals, whether here legally or illegally, are not EVEN U.S. CITIZENS! Not to mention natural born citizens. No matter what the courts say.
One of Arthur's parents and, supposedly, one of Obama's parents was a foreign national; neither was a foreign minister or ambassador from their respective countries.
The 14th Amendment history article you cite quotes the author of the citizenship clause of that amendment as stating that every person born within the limits of the United States is a citizen of the United States, with the singular exception of the children of foreign ambassadors. Arthur and (maybe) Obama are thus citizens of the United States. The author's statement indicates that they are citizens by virtue of natural law and national law. But does that make them natural born, according to the doctrine of original intent? Does the intent of the authors of the Fourteenth Amendment supersede what the Framers of the original Constitution intended?
If Senator Howard's view is correct, that means that the children of illegal aliens are U.S. citizens by virtue of their birth. Thus, they cannot be expelled any more than someone whose parents were native born.