If the illegal alien parents are from Mexico then the new baby born here is Mexican..a citizen of Mexico...
Regrettably, you are mistaken.
Regardless of where the parents are from, or the circumstances of their presence on American soil, a child born on American soil is an American citizen.
That judgment is based on a SCOTUS decision regarding the 14th Amendment.
Consequently, it will take a SCOTUS decision or a Constitutional Amendment to change it.
You are correct that the children are also Mexican citizens at birth, due to the nationality of their parents. But, the fact remains, they are also American citizens by virtue of their birthplace.