The 14th Amendment of 1866 states:
All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside.
This amendment was put forth during a reconstruction period after the Civil War and was to provide slaves the ability to claim their citizenship along with all other residents of the United States.
The intent was not to allow pregnant foreigners to enter the country with the intent of giving birth to get a US citizenship for their child. A child who could later bring their parents into the country. See ABC News recent story on the tropical island of Saipan, which is a US territory.
ABC News reported in December 2012, Chinese Women Pay to Give Birth at California Maternity Mansion.