Clearly the term "America" either disambiguates to a continent or a country, and most assume the country.
"Europe," on the other hand, really is a continent, so the term has a completely different meaning than the EU, although it would be reasonable for the two to be synonymous eventually, they clearly are not currently.
Anyway, it seems reasonable to use the term America as shorthand, instead of U.S.A., as it's pretty obvious what you mean.