The Constitution is very clear on citizenship. Citizenship is mentioned in Article 1, Section 2, Article 1, Section 3, Article 1, Section 8, Article 2, Section 1, and in the 14th Amendment and several subsequent amendments. Most importantly, lets look at citizenship as it's defined in the 14th Amendment: "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."
Born or Naturalized. Born or Naturalized. That sounds pretty specific. I didn't see "sneaked across the desert in the dead of night" or "waded across the Rio Grande" or "tunneled under the fence" in there anywhere.
Now where in the hell does Obama come up with the idea that "being American is not a matter of blood or birth"? Constitutional scholar, my ass.