"Every Person born within the limits of the United States, and subject to their jurisdiction, is by virtue of natural law and national law a citizen of the United States. This will not, of course, include persons born in the United States who are foreigners, aliens, who belong to the families of ambassadors or foreign ministers accredited to the Government of the United States, but will include every other class of persons."
Since illegal aliens are foreigners their offspring should not be granted automatic citizenship either unless Congress, like in 1924 grants it to them.
This issue was settled a long time ago.