The 14th amendment covers citizenship like this:
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.
The author of the amendment did not mean to make citizens of children born to foreign citizens currently residing on US soil:
The author of the 14th Amendment Citizenship Clause, Senator Jacob M. Howard, stated, in reference to the Amendment, "This will not, of course, include persons born in the United States who are foreigners, aliens, who belong to the family of ambassadors, or foreign ministers accredited to the Government of the United States, but will include every other class of persons."
But as with most other things Washington and our courts touch, plain common sense has been corrupted so that now children of illegal aliens become citizens. This is wrong on many fronts, rare in the world (only about 30 countries and hardly any modern Western countries do this), and provides a tempting incentive to break U.S. immigration law.
Those who want to change this talk about tweaking the 14th amendment itself. Good luck with that. There are enough blue states legislatures that want future Democrat voters that this approach will go nowhere. Better, and sufficient, would be to have Congress define who is subject to its jurisdiction for purposes of the 14th Amendment.
Some say that wouldn’t survive a court challenge. I suspect it would face trouble in plaintiff shopped lower courts, but do just fine at the Supreme Court.
We need to do something, and since a Constitutional amendment isn’t feasible, passing a law is the correct next step.