Interesting that "United States" was popular for quite a while, but has declined in use since the 80s. "United States of America" was fairly steady in use for 100 years, but rose sharply in the 1910s. "USA" barely seemed in use at all until the Civil War, and since the 70s, the decline in the use of "United States" has been inverse to the growth in "USA".

(Been reading a lot of news articles about Congress today. Probably accounts for the word choices.)