The reverse situation actually exists IOTL. Citizens of the United States habitually refer to themselves as Americans, implying thereby that residents of South America, Central America, Mexico and Canada are not Americans, despite the fact that they too live in the Americas. South of the border they refer to themselves as Mexicanos and US citizens as Norteamericanos, despite the fact that they too live in North America.
I've always seen this issue in this way: When referring to the country I'm from (United States), I call myself an American.* When referring to the continent that I'm from, I call myself a North American. Using that logic, then someone from Brazil or Argentina would be a South American just as a Canadian or Mexican would also be a North American like people from the United States. So really, it could be said that there is little need for those outside the United States to refer to themselves as Americans. They are either North or South Americans. Now, that's not perfect, I'll admit that. It may leave some dissatisfied. But that's how I've always seen it.
Now on topic, I think that in OTL, the term "Yankee" has become the most common term in referring to those who are US Nationals on the international scene. Yet in reality, it only means those who live in the Northeastern US and Great Lakes Regions.
*Let's be honest though. I'm living in the Unitedstatsian occupied Republic of Michigan. So really, I'm a Michigander or Michiganian