Obviously they can be deported. Even if you don't consider circumventing border security and US customs a hostile action, they forfeit any rights granted under US jurisdiction by refusing to enter and/or stay in the country legally. This also applies to those who overstay their visas.

"under US jurisdiction", you say?  Checkmate. 

What the hell are you talking about? They forfeit rights that they would have under US jurisdiction because they're not under US jurisdiction in those situations. Stop being dense.

Let's get down to brass tacks here.  What do you imagine is meant by the word "jurisdiction"? 

I imagine it to mean the area and people over which the United States has full legal authority and power, which I believe includes illegal immigrants.  That is, I believe Mexico doesn't have the legal right to interfere with what the USA does with a Mexican who illegally immigrated to the United States.  Diplomats are an example of a group in the United States but not fully subject to its authority; their diplomatic immunity means that they cannot be held accountable for crimes without their country's permission.  The only thing the USA can do is expel them from its territory. 

We can look at the contemporary laws at the time of the Fourteenth Amendment to see what they meant by jurisdiction. The Civil Rights Act of 1866 states that "all persons born in the United States and not subject to any foreign power, excluding Indians not taxed, are hereby declared to be citizens of the United States." If someone from Mexico illegally enters the United States, they are still subject to Mexico, and any children they give birth to are Mexican subjects as well. You are still considered to be under the jurisdiction of your home country while abroad, which is why you can be prosecuted for US crimes in another country. Taking all this into account, the courts could certainly use legal precedent to rescind birthright citizenship to illegal aliens, if not all aliens.

Of course, that assumes that courts need any sort of precedent or legal arguments at all. Like I said, if abortion rights can be pulled out of thin air, anything goes. Thanks, judicial activism!

Just because the US still cares if its citizens commit crimes abroad doesn't mean that they have the authority to go over there and arrest them.  Either the government has to work with the foreign government in question or just wait until the criminal comes home, AFAIK.  So I have to disagree with your analysis of which nation can be fairly said to "have jurisdiction" over that person at that time.  I'm not a lawyer, though. 

When the constitutional amendment in question was being written, I have a well-sourced article reporting that its framers were concerned with excluding diplomats and quasi-sovereign Indians, and no one else.  In fact, if I recall correctly, the US didn't even have laws limiting immigration at the time!  (I may be misremembering something here, please correct me if that's wrong.) 

The only other Supreme Court involvement on the issue is a footnote in a 1982 decision in the case Plyler v. Doe, which dealt with the issue of whether states must provide education to children not “legally admitted” into the United States. In that case, Justice William Brennan, writing the majority opinion in the 5-4 decision, stated that “no plausible distinction with respect to Fourteenth Amendment ‘jurisdiction’ can be drawn between resident aliens whose entry into the United States was lawful, and resident aliens whose entry was unlawful.”

Considering that this argument of yours flies in the face of current precedent, aren't you the one on the side of radical judicial activism? 

And going back to what you bolded, it doesn't seem to me that you actually directly addressed this question:  if the USA is, for example, prosecuting and potentially jailing an illegal immigrant from Mexico, what power does Mexico have over the USA's actions? 

Yes, neither of us are lawyers. I'm not making a foolproof legal argument here. At this point, we should agree to disagree.

The definition of jurisdiction is "the official power to make legal decisions and judgments" or "the extent of the power to make legal decisions and judgments." It doesn't really say anything about the ability to act upon any legal judgments, so Mexico would still technically have jurisdiction over Mexican nationals in the United States. A case can be made for either side.

I guess in the technical sense, no federal law restricted immigration, but naturalization law limited citizenship to "free white persons of good moral character".

https://en.wikipedia.org/wiki/Naturalization_Act_of_1795

After 1870, Africans could also become naturalized citizens, but the logistics of native Africans crossing the ocean prevented any surge of immigration. In 1882, Chinese immigrants were banned, and the national quota system was implemented in 1924, which heavily favored those from the British Isles and Germany. US immigration was explicitly white from 1790 to 1965.

And, yeah, in this case I would be on the side of judicial activism. It's equally available to both sides of the political spectrum, after all.

1.  So you are saying that Mexico and not the United States has power to make legal judgments regarding illegal immigrants from Mexico and their children? 

2a.  OK, but that has nothing to do with my point, which was that the amendment could not have been intended to exclude the children of illegal immigrants if there was no such thing as illegal immigration. 

2b.  As for racial restrictions on immigration and naturalization, notice how blacks were for a time able to be born into citizenship but not able to naturalize?  Naturalization citizenship and birthright citizenship are two different issues.  And immigration is yet another topic.  These are related to one another, of course, but on the other hand they should not be conflated. 

3.  So you have no problem with judicial activism, just with results of it that you happen to dislike?  I just want to clarify because there are a lot of people who claim to hate judicial activism on principle. 

There is of course no obligation on your part to continue a discussion you no longer want to participate in, but I think it's very wrong to say that we had exhausted the points of debate that could be reasonably argued by laymen. (I don't think we were at the point of simply having to agree to disagree.)

No, there's really no reason to debate this any further. You want illegal aliens to stay in the country and their children to have citizenship, while I don't. You want whites to be a minority in the country that they built, while I don't. I can see that your opinion won't be changed, and neither will mine.

I'll answer your last question, though. I don't have a problem with judicial activism anymore. The Right sticks to its principles, while the Left plays dirty. This is why the Right always loses. Well, now we've decided to stop losing.