14th Amendment:
"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."
There are rumblings about "subject to the jurisdiction thereof" somehow excluding folks based on their immigration status, but frankly, the meaning is clear, and jurisprudence recognizes this. The jurisdiction carveout is for international diplomats, i.e. people who are literally not subject to US law. Immigrants, even illegal immigrants, are subject to US law. Stating otherwise would have vast repercussions.