Unlike if, say, Joe Biden (both of whose parents were U.S. citizens) had been born in Kenya, Barack Obama would not have been a U.S. citizen at birth had he been born in Kenya (assuming that his father was Barack Obama, Sr.). Back in 1961 (and until the federal law was amended in 1986), a person born abroad with one U.S. citizen parent and one alien parent would be a U.S. citizen at birth if the U.S. citizen parent had, as of the date of such birth, resided in the U.S. for at least 10 years during his or her life, with at least 5 of those years of residency having come after turning 14. Well, guess what? Obama’s mother (and only U.S. citizen parent), Stanley Ann Dunham, was only 18 years old when Obama was born, so it would be mathematically impossible for her to have resided in the U.S. for 5 years after having turned 14. So if Obama was born in Kenya, or anywhere else outside of U.S. territory, he would not have been a U.S. citizen at birth. This would mean that (i) unless he became a naturalized U.S. citizen at some point in his life (of which there is no evidence), he would not be a U.S. citizen today, and thus illegally served in the U.S. Senate and broke countless other laws, and (ii) even if he later became a naturalized U.S. citizen, the fact that he wouldn’t be a U.S. citizen at birth would mean that he isn’t a natural-born citizen of the U.S. and thus would not be eligible to serve as president.
So, yes, it would be a huge deal if Obama actually had been born in Kenya.
Birth Abroad Out-of-Wedlock to a U.S. Citizen Mother:
A person born abroad out-of-wedlock to a U.S. citizen mother may acquire U.S. citizenship under Section 309(c) of the INA if the mother was a U.S. citizen at the time of the person’s birth and if the mother was physically present in the United States or one of its outlying possessions for a continuous period of one year prior to the person’s birth. The mother must be genetically related to the person in order to transmit U.S. citizenship.