"They" say that Section 1 of the 14th Amendment establishes a birthright to citizenship. Trump intends to challenge the extension of this law to illegal immigrants with an executive order. The Courts will make the final decision.

Section 1. 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. No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.