Suppose that the Republic of Togo's legislature, or whatever the hell they have, voted to consider all Americans to be citizens of Togo. Would anyone be eligible to be president?
I've been saying this for ages. I even posited the hypothetical here a couple of weeks back. I got this as a response: "you chose to posit a ridiculous hypothetical. Let’s play....what are the odds that the UK will grant everyone born in the US dual citizenship?"
But, there could be some element of doubt, so those who responded negatively to you could possibly have a point. The reason a citizenship claim upon you could introduce doubt as to your being a natural born citizen under the Constitution would be the potential legal claims upon you, by Italy, when outside the jurisdiction of the United States, posing a difficulty for you and in turn the nation, should you become President.
The same would potentially be true, had you been born to two citizen parents in a foreign nation that itself claimed you as a citizen by birth under jus soli.
Obama does not have two citizen parents, and so U.S. jurisdiction was incomplete at birth, which is why you've seen so much parsing of the phrase "subject to the jurisdiction thereof." A foreign citizenship claim upon him only increases the level of doubt, as to his status at birth. That such a claim apparently did, and perhaps still does, exist, by the British, makes for a very compelling argument, but the fact that the citizenship is there, or is not, is not really relevant. It's the fact that his father was foreign and not a citizen, that is the problem.