Some people apparently take offense at the way citizens of the(se) United States call themselves Americans as opposed to United Statesians.
My response to the Latin Americans among these would be to say, "You had your chance, but decided to act French, instead."
Also, Americans had a strong tradition in identifying themselves with the particular State they lived in, often calling themselves Carolinian, or Virginian, or New Mexican, or Texan. This attachment was nostalgic, and focused on smaller communities with more peculiar cultures. Only now, some 4 or 5 generation after the Civil War, are these notions beginning to subside, along with ease and frequency of emigration.
I, personally, prefer to identify myself as a New Mexican, though I was born in New England and have lived in North Carolina for 10 years now.