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"common sense tells me" is usually not applicable in a court of law. Unfortunately, or fortunately, the concept of "natural born citizen" is never addressed, let alone defined, in US law anywhere else but that mention in the requirements for President. On the contrary, naturalized citizenship is rigorously defined, and Obama does not meet that definition at all. In fact, having been involved in debates regarding the possibility of children adopted from foreign countries to become President, I can assure you that there seems to be a reasonable case to be made that such children fall under the classification of "natural born citizen", since they definitely do not fall under the definition of naturalized citizens, and instead are provided with American birth certificates after they are adopted by American citizens. That being at least up for argument, being born to an American parent abroad who did not reside in the US quite long enough after age of majority would seem to be not the unbeatable objection some seem to think. On the other side of the question, there are those who hold that the definition of "natural born citizen" in fact excludes all children born to American citizens abroad.
So, even if Obama was born in Kenya; and even if his mother did not live in the US the requisite time after her majority; the worst that would lead to is a legal challenge to a definition which has not in the past been enforced in the most restrictive definitions possible.
Of course, that's what the rightwing extremists are after; if they could get Obama disqualified that would be a nice but unexpected Christmas present for them, but the real tactic is to hamstring the legally elected President of the US with an endless string of legal harassment, as seen in the Clinton presidency, in the belief that although me may be legally elected, he can't possibly be legitimate. The converse being the Bush "victory" in 2000. In the minds of these people, anybody who doesn't buy into their tribal dogma is not a "real" American, and any President who wasn't selected by them isn't legitimate. Of course, if this attitude isn't so intuitively obviously correct to you that you need to have it spelled out like this, you Hate America.