Man loves to constantly reference the 1700s era of laws

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For him to do this, he would first have to legally designate which nations are enemies of the US; he can't pick and choose individually who he wants to deport in this scenario.
He would first need to establish such individuals and entities are either deemed to be dangerous, found making malicious statements against the US, and/or conspiring against the US government in terms of seizing control/overrunning the country through violent measures (think Taliban in Afghanistan type of scenario), and simply breathing and crossing the border illegally doesn't exactly fall under those categories.