Progressives are screaming, but at this point, their screams are drowning out their other screams, so let's cut to the chase.
What US law says:
The following shall be nationals and citizens of the United States at birth:
(a) a person born in the United States, and subject to the jurisdiction thereof; Source: 8 USC 1401
What the US Constitution Says:
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.
Source: 14th Amendment, US Constitution
What 14th Amendment drafter U.S. Senator Jacob Howard said in floor debate:
“This will not, of course, include persons born in the United States who are foreigners, aliens, who belong to the families of ambassadors or foreign ministers accredited to the Government of the United States, but will include every other class of persons.”
Source: Congressional Globe
What the Supreme Court Said in 1873:
The phrase, "subject to its jurisdiction" was intended to exclude from its operation children of ministers, consuls, and citizens or subjects of foreign States born within the United States.
Source: Slaughterhouse Cases
What the Supreme Court Said in 1884:
Source: Elk v. Wilkins
Congressman Steve King has a short treatise on this issue posted at his website. Please take five minutes to read it:
Ending Birthright Citizenship Does Not Require A Constitutional Amendment
Andrew McCarthy makes a similar argument regarding "Jurisdiction:"
Constitution Does Not Require Birthright Citizenship
Finally, Tony Mecia at the never-Trumper outhouse The Weakly Standard, makes a weak case for the opposition, citing a case of an American man of Chinese descent who had to fight for his citizenship all the way to the Supreme Court. His parents were from China, but wait for it... They were permanent legal residents of the US at the time of his birth. That's the best they got, folks.
What say you?
Revoking Birthright Citizenship Enforces the Constitution
Birthright Citizenship and its Allies