Donald Trump's recent comments on how he would end the practice of giving anyone born on U.S. soil (unless doing duties for a foreign government) automatic citizenship has led me to voice my opinion on this issue. I am against birthright citizenship, but not because I am racist, xenophobic, or have anything against Mexicans or any other nationality. It is because, similar to how increases in health-care technology (and the costs associated with patients using such) has rendered the idealistic concept of "free-market healthcare" an anachronistic economic liability, advances in travel (and to a lesser extent changes in gender roles) has rendered the once-closely-linked concepts of "physical place of birth" and "nationality at birth" less directly correlated with each other.
"Physical place of birth" is just that - the place where you were born at. If that was at or near the location of your parents' permanent residence than that also describes your "homeland" - where you likely grew up and your first memories were founded. Before easy long-distance travel via automobiles and airplanes was common, and when it was rare for a woman to be away from her homeland for career purposes, that correlation served true for almost all births.
"Nationality at birth" describes what country or countries you have been considered a subject of since when you were born. It makes sense, and should be the case, for you to be considered a subject of the place where you were actually born in IF that's where your parents had a legal and permanent residence. However, if your parents had violated the country's immigration laws to get there, or if they were in the country just visiting or on some other temporary basis, then the parents' children should NOT automatically be entitled to be considered a subject of that country (but would usually be a subject of the home country or countries of the parents - in the rare cases where that isn't the case and the child would be otherwise stateless an exception can be made). For those cases where the child spends a significant part of their childhood in the U.S., I would have a provision if you lived a certain number of the first 18 years of your life in the country you'd be entitled to citizenship upon request once an adult - but nothing for the parents who were here illegally and/or temporarily.
I should also note that there are MANY countries in the world that once had birthright citizenship that do not anymore for the reasons I have described (here is an article about when the last holdout in the EU, Ireland, did away with it in 2004). Also, we may not have to amend the Constitution because so far the only definitive cases (e.g. Wong Kim Ark) have dealt with parents who had permanent residence (which I do agree that those children should be citizens) - an historic precedent is that Native Americans were not automatically citizens until 1924).