[caf]

What exactly is the term that this group of people would use for themselves, in a context where they want to be clear that they are referring to nationals of the USA specifically?

(On reflection, how does "US American" strike you? This seems analagous to "South Korean" or "Mainland Chinese")

[bluedanieru]

There is no ambiguity in 'American'. At best, there exists among some people the belief that there should be ambiguity where none exists.

Go strike up a conversation with anyone in the world and refer the people from the New World as 'Americans'. That person will assume you are referring to US citizens. Now, should the issue be forced somehow you will have to explain that, in fact, you were referring to folks from the New World all along, not so-called US Americans specifically. That person will then probably roll their eyes a bit.

So it's a moot point. You're trying to resolve a confusing situation that has virtually no chance of ever actually occurring, where in fact your solution would actually introduce confusion.

[eftpotrm]

But, there is arguably no more commonality between the people of Norway, Portugal and Bulgaria than between Canadians, Mexicans and Chileans, so why can we call the first group collectively European but not the second collectively American?

The standard English nomenclature for residents of the USA (which I belive isn't so much of an issue in other languages) is confusing.

[bluedanieru]

I'm not making any claim that it's logical or follows a pattern. Are you sure you really mean "confusing" though? As in, ambiguous? Because it really isn't for most people, even those that don't speak English very well.