My research shows that that amendment was adopted in 1986 and therefore it was not in effect in 1961 and thus while it would make a person a citizen at birth, it would not make a person a "Natural Born" Citizen.
Thus while it would make Obama a Citizen, it would not give him "Natural Born" status. It would simply give him "Ex-Post Facto Legislatively Mandated Citizenship at Birth" status.
The 1790 Alien Naturalization Act, enacted by Congress on Mar. 26, 1790, dictated the following:
“Be it enacted by the Senate and the House of Representatives of the United States of America in Congress assembled, That any alien, being a free white person, who shall have resided within the limits and under the jurisdiction of the United States for the term of two years, may be admitted to become a citizen therof, on application to any common law court of record, in any of the states wherein he shall have resided for the term of one year at least, and making proof to the satisfaction of such court, that he is a person of good character, and taking oath of affirmation prescribed by law, to support the constitution of the United States... And the children of such persons so naturalized, dwelling within the United States, being under the age of twenty-one years at the time of such naturalization, shall also be considered as citizen of the United States. And the children of citizens of the United States, that may be born beyond sea, or out of the limits..., shall be considered as natural born citizens...”