The law in effect in 1961 was the 1952 Nationality and Immigration Act commonly called the McCarron - Walters Act.
http://library.uwb.edu/guides/usimmigration/66%20stat%20163.pdf
TTTLE III - NATIONALITY AND NATURALIZATION
CHAPTER 1 – NATIONALITY AT BIRTH AND BY COLLECTIVE NATURALIZATION
NATIONALS AND CITIZENS OF THE UNITED STATES AT BIRTH
Sec. 301 (a) The following shall be nationals and citizens of the United States at birth:
(1) a person born in the United States, and subject to the jurisdiction thereof;
Sec. 301 (a) (7) A person born outside the geographical limits of the United States and its outlying possessions of parents one of whom is an alien, and the other a citizen of the United States who, prior to the birth of such a person, was physically present in the United States or its outlying possessions for a period or periods totaling not less than ten years, at least five of which were after attaining the age of fourteen years;”
Obama born in Hawaii comes under Section 301 (a) (1).
Obama born in Kenya comes under Section 301 (a) (7).
Thank you very much.