Alexander Hamilton- who wrote a great musical about himself, btw- didn't have the option of being president- he was born in what is now St. Kitts and Nevis, which made him an immigrant, and was ineligible to serve under the terms of the newly adopted constitution. Which raises the question- did they put the "you have to be a citizen-by-birth to be president" thing in there just to keep HIM out of the job?