The most important part of her column she recaps the relevant Supreme Court cases bearing on the Court's interpretation of the 14th Amendment, the relevant portion of which says that, "All persons born or naturalized in the United States and subject to the jurisdiction thereof, are citizens of the United States and of the state wherein they reside."
Here are the Supreme Court opinions Coulter cites:
Supreme Court opinion in the Slaughterhouse cases (1873):Of all the developed countries in the world only the U.S. and Canada confer citizenship on children born on our soil. It's a policy based upon a distorted reading of the Constitution and supported by Democrats because they want Hispanic votes and by Republicans because they want cheap labor.
“(N)o one can fail to be impressed with the one pervading purpose found in (the 13th, 14th and 15th Amendments), lying at the foundation of each, and without which none of them would have been even suggested; we mean the freedom of the slave race, the security and firm establishment of that freedom, and the protection of the newly-made freeman and citizen from the oppressions of those who had formerly exercised unlimited dominion over him.”
Supreme Court opinion in Ex Parte Virginia (1879): “[The 14th Amendment was] primarily designed to give freedom to persons of the African race, prevent their future enslavement, make them citizens, prevent discriminating State legislation against their rights as freemen, and secure to them the ballot.”
Supreme Court opinion in Strauder v. West Virginia (1880): “The 14th Amendment was framed and adopted … to assure to the colored race the enjoyment of all the civil rights that, under the law, are enjoyed by white persons, and to give to that race the protection of the general government in that enjoyment whenever it should be denied by the States.”
Supreme Court opinion in Neal v. Delaware (1880) (majority opinion written by Justice John Marshall Harlan, who was the only dissenting vote in Plessy v. Ferguson): “The right secured to the colored man under the 14th Amendment and the civil rights laws is that he shall not be discriminated against solely on account of his race or color.”
Supreme Court opinion in Elk v. Wilkins (1884): “The main object of the opening sentence of the 14th Amendment was … to put it beyond doubt that all persons, white or black, and whether formerly slaves or not, born or naturalized in the United States, and owing no allegiance to any alien power, should be citizens of the United States … The evident meaning of (the words, “and subject to the jurisdiction thereof”) is, not merely subject in some respect or degree to the jurisdiction of the United States, but completely subject to their political jurisdiction, and owing them direct and immediate allegiance. … Persons not thus subject to the jurisdiction of the United States at the time of birth cannot become so afterward, except by being naturalized …”
One has to leap forward 200 years from “the founding of the republic” to find the first claim that kids born to illegal immigrants are citizens: To wit, in dicta (irrelevant chitchat) by Justice William Brennan, slipped into the footnote of a 5-4 decision in 1982.
As Coulter points out 70% of illegal aliens are being subsidized by American taxpayers. Coulter is a big Trump fan largely because Trump promises to end birthright citizenship, but beyond his populist Huey Long-type rhetoric there's no reason in his history to think he will. It's almost certain, however, that no Democrat president will end it.