This is unconstitutional and based on incorrect comprehension of the 14th amendment. Gaetz is specifically leaning on the "and subject to" part in "born or naturalized in the United States, and subject to the jurisdiction thereof.”
However, this is clearly referring to exclude children born to diplomats who are not subject to jurisdiction because of diplomatic immunity. The exclusion does not apply to children born to undocumented immigrants.
Warrants are required for U.S. Mail. Likewise, the government should not have warrantless access to all electronic communication. It's an outrageous position.