The answer to this question is not crystal clear, but it seems unlikely.  The dispute hinges around the long-standing interpretation of the 14th Amendment to the U.S. Constitution, which reads, in relevant part:

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.

President Trump claims that children born in the United States to non-immigrants or undocumented aliens are not “subject to the jurisdiction” of the United States, and thus, are not entitled to U.S. citizenship by virtue of their birth within the territorial borders of the United States.  Given this interpretation, President Trump argues that he could declare, by executive order, that federal agencies no longer interpret the 14th Amendment to permit blanket birthright citizenship to all who are born within the United States.

Many legal scholars believe that President Trump’s actions are completely without merit and are contrary to long-standing legal interpretation of the 14th Amendment. They maintain that a constitutional amendment would be necessary to take away birthright citizenship.  This makes perfect sense, as the United States will certainly charge anyone in the United States with a crime, if committed, which it can only do if the United States has jurisdiction over them.

In sum, it seems highly unlikely that President Trump can end birthright citizenship by Executive Order, and if he attempted to do so, it would surely face immediate legal challenge.

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