2. The left is filling up comment streams with cries of "unconstitutional!" They are wrong. Neither approach proposes to change the Constitution. Instead, they would change how one phrase in the 14th amendment is interpreted: "and subject to the jurisdiction thereof".
3. The person who inserted that phrase in the 14A made it clear that the purpose was to keep it from being applied to "persons born in the United States who are foreigner, aliens, …" That is exactly the issue being addressed.