LOL! That's a new one. An American mom gives birth to a child on an American soil and the baby's not a citizen? If only his mom had just said she didn't know who the father was, he could've been an NBC? Missed it by that much!
When the nation was founded, the citizenship of the woman was irrelevant. The Common Law at that time was that marriage automatically naturalized a woman to her husbands Allegiance. I believe a statutory law mandating this was passed in 1857, but I don't remember for sure.
At the time, all the governments believed that not only did marriage give a woman a new name, it gave her the husband's national character as well. Foreign women married to American men were automatically naturalized (And with no ceremony, DoodleDawg) and so therefore both parents were always American citizens if the father was.
Foreign men married to American women also naturalized those women to his country of allegiance. Again, this condition was COMPELLED by American law at one point.
My point here is, this "Women's Lib" stuff is relatively new, and does not at all accurately reflect the conditions of earlier times.
By the rules in effect in 1787, Rich Santorum's mother would be regarded as Italian by our government once she married an Italian Citizen.