From Wikipedia, prior to deletion the dicdef entry there:
A U.S. term, usually used to refer to a pointless or unproductive activity. "Dixie" was the unofficial battle song of the Confederates in the American Civil War. If you "whistle Dixie," you are singing the battle cry of the army that lost, a useless act. If it is said that you are not whistling Dixie then it means that there is validity to what you have said or what you are doing.
Often used in the context "I ain't just whistling Dixie," meaning "I am very serious about this."
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Rfv-sense: To engage in pointless activity. The idiom is about pointless conversation AFAIK. DCDuringTALK * Holiday Greetings! 18:41, 27 December 2009 (UTC)
I've got at least one citation that does not require speaking, but I'm not sure it truly supports an additional sense:
2008, Thomas F. Schaller, Whistling Past Dixie: How Democrats Can Win Without the South, page 1
[A]nyone who believes Democrats can consistently win the White House without puncturing the Republican dominance across the South is just whistling Dixie. —Los Angeles Times columnist Ronald Brownstein