That isn't what that meant when the 14th Amendment was enacted. OF COURSE anyone within our jurisdiction is subject to our laws, but one the intents of the 14th Amendment was to assure that former slaves AND their children would be treated as United States citizens as they were in fact subject to the jurisdiction of the United States. In other words they were not stateless persons after they were emancipated; they were not automatically in a no mans land not knowing if they were now citizens of the U.S. or citizens of some African nation most were not even still able to know which ones they originated from.
When a Mexican woman plops out a kid on our soil she is still a Mexican citizen--- so her kid should be one too. And the test for that is that if she wants to return to Mexico and take the kid, Mexico considers that child a Mexican citizen who is subject to the jurisdiction (speaking of citizenship jurisdiction) of Mexico. If a diplomat's wife has a child here in the USA is that child automatically a US citizen? No it is not.
Illegal immigrants may be "required to" do many things but most don't follow the laws. The first one of course not come here illegally in the first place. Then after that the almost sickening way many of them steal or fraudulently use social security identification that is not theirs. A felony which SHOULD result in immediate removal and deportation when found out, AND then NEVER being allowed to return or apply for citizenship under any circumstances; a punishment for their fraud.
Now if you want to talk about a foreign national who is willing to serve in the military for lets say at least ten years and then EARN citizenship, then I am okay with that. Sort of the way the French may grant citizenship to those who served in the French foreign legion. I have no issue with someone honorably EARNING citizenship. But stealing it, screw that! Send them home!
And btw, "there ain't no draft no more".