Here is an interesting discussion of US versus U.S. versus USA versus U.S.A. from Wikipedia: Manual of Style:
In American and Canadian English, U.S. (with periods) is the dominant abbreviation for United States. US (without periods) is more common in most other national forms of English. Some major American guides to style, such as The Chicago Manual of Style (16th ed.), now deprecate U.S. and prefer US. Use of periods for abbreviations and acronyms should be consistent within any given article, and congruent with the variety of English used by that article. In longer abbreviations (three letters or more) incorporating the country's initials (USN, USAF), do not use periods. When the United States is mentioned with one or more other countries in the same sentence, U.S. or US may be too informal, especially at the first mention or as a noun instead of an adjective (France and the United States, not France and the U.S.). Do not use the spaced U. S., nor the archaic U.S. of A., except when quoting. Do not use U.S.A. or USA, except in a quotation or as part of a proper name (Team USA), as these abbreviations are also used for United States Army and other names.
The Chicago Manual of Style, 15th Edition (2003) comes out strongly in favor of spelling out United States (rather than abbreviating it) when the term is used as a noun and not an adjective:
15.34 "U.S." or "US." Except in scientific style, U.S. traditionally appears with periods. Periods may nonetheless be omitted in most contexts, Writers and editors need to weight tradition against consistency. In running text, the abbreviation (in either form) is permissible when used as an adjective, but United States as a noun should be spelled out.
Words Into Type, Third Edition (1974) takes an even stronger anti-abbreviation position:
In the most formal writing, United States should always be spelled out; in other works U.S. is gaining currency as an adjective when preceding a government agency, department or organization or the name of a government vessel. [Examples omitted.] When used as an adjective with general terms, United States should be spelled out. [Examples omitted.]
Both Chicago and Words Into Type have so little regard for USA that they don't even mention it as an option in their discussions of abbreviations for countries.
The Associated Press Stylebook (2006), however, accepts both U.S. and USA as nouns, and seemingly views them as equally valid designations:
U.S. The abbreviation is acceptable as a noun or adjective for Unites States.
USA No periods in the abbreviated form for United States of America.
Nevertheless, I have never seen a style guide that approved of using USA as an adjective.