What Mark Levin said is the Supreme court has never ruled that children of illegals are American citizens. So this statement is false.
He also says there's another part of the Constitution. It's article 1, section 8, clause 4. It says in plain English. "The Congress shall have power to establish a uniform rule of naturalization."
Levin says "Now, you know what that means? That means Congress, not the courts, not the president, not ICE -- it means the United States Congress has the power to regulate immigration in this regard."
Congress has the power to regulate naturalization. ie, when people born outside the United States seek to become U.S. citizens but the 14th Amendment (which was ratified after Article 1, section 8, clause 4 and thus would amend it if there was a conflict) guarantees 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.” 14th Amendment, Section 1.
The Supreme Court has never held a case specifically about the children of illegal immigrants. However, the Supreme Court did have a case where it determined that a child born to a foreign immigrant in the U.S. was a citizen (United States v. Wong Kim Ark, 169 U.S. 649 (1898)).
In Wong Kim Ark, a Chinese laborer was brought over to help build a western railroad, had a child, and then returned to china. The child later wanted to return to the U.S. claiming that he was a citizen but the U.S. congress had recently passed the Chinese exclusion act and tried to keep him out claiming that he was not a U.S. citizen since he had been born to a foreigner. The Supreme Court ruled based on the 14th Amendment that he was a citizen because (1) He was born in the U.S. and (2) His father had been subject to the jurisdiction of the U.S. because he had been subject to the laws of the United States while he lived in the United States unlike a diplomat who has diplomatic immunity from U.S. law.