Read the Constitution and Bill of Rights and note where it says "citizen" and where it says "person."
Pay special attention the the 14th Amendment and the Equal Protection Clause.
Read Plyler v. Doe where the Supreme Court found that Illegal Aliens fall under the Equal Protection Clause and are thus protected as persons in the Constitution.
The Bottom line is that Illegal Aliens have the same Constitution Rights as Citizens.
Again this is not what I advocate but rather what is fact.
So the founders were OK with a ship slipping in under the cover of darkness, and one hundred passengers spilling out and marching in protest up the streets of New England? Good to go?