Your statement illustrates your belief that illegal aliens are subject to jurisdiction. Thus, if and when their children are born, the children are US citizens. This was decided eons ago - it’s a non-starter and waste of time. The only way around this would be to amend the constitution, and the odds of that happening are about the same as me walking on the moon.
Can the invaders vote? Are they required, by law, to pay taxes? If so, how without a SS#?
Jurisdiction doesn't mean what you think vis-a-vis the 14th Amendment.
Clearly you have a stake in providing these invaders citizenship. Care to tell us what that is?