Congressman Billybob was wrong about the 14th in the following respect: It actually forbids anchor babies because the 14th only applies to those "subject to the jurisdiction," not those merely within the jurisdiction. Hence, because the Constitution is a limiting document, Congress has no power to confer citizenship on those within, but not subject to the jurisdiction of the United States.
Any alien, resident or illegal, is within, but not subject to the jurisdiction of the United States. All you have to do is read a law dictionary contemporary to the time the Amendment was drafted to see how those who wrote and ratified it understood the word "subject."