Okay, I dropped what I was doing and called the Mark Twain Papers & Project at the University of California, Berkeley. Turns out Twain’s “The Czar’s Soliloquy” (1905) includes the line that ” ‘…the true patriotism, the only rational patriotism, is loyalty to the Nation ALL the time, loyalty to the Government when it deserves it.’ “
When I searched Nexis for Obama’s version of the quote, that patriotism “is supporting your country all the time, and your government when it deserves it,” the citations I got seemed to stem from an anti-Iraq war documentary made by the left-wing filmmaker Robert Greenwald, in which a former CIA officer says, “Mark Twain’s definition of patriotism is — patriotism is supporting your country all the time and your government when it deserves it.” (I have a transcript of the movie, Uncovered, because I did a chapter on Greenwald and political documentary in my book.) Although there may have been some other source of that particular misquote — it also appears in Wikipedia — it appears that Twain’s thoughts on patriotism became somewhat common in some circles of the left after that.