The Far Side

Sorry if I over explain anything obvious...

"Whistling Dixie" is a local American term generally meaning not being serious all the way to over-hoping for a good outcome. As in, "If you think the president is going to apologize, you're whistling Dixie."

The term refers to the song Dixie which was basically the anthem for the South/Confederacy in the US Civil War. It's a very catchy tune and can be danced to or marched to because of its meter.

In the comic, the outnumbered soldiers who are hiding are southern confederates, with a northern Union regiment marching on their position. This probably wouldn't be a good time for the losers hiding in the ditch to give away their position by whistling their anthem. But man, it is a catchy tune and that regiment really is drumming a beat.

The actual term "whistling Dixie" probably came much later than the civil war, because it was referring to the southerners' dreams of winning being crushed, but that's classic Far Side juxtaposition.

I think that's probably enough explanation for the comic, but for background:
The song itself was written for American minstrel shows, which heavily used blackface and were often used to push and popularize racist stereotypes about African Americans. The song is basically about a free former slave pining to be back on the plantation, and is pretty much saying that's where black people belong.

You can find some examples of alternative lyrics in other comments, some of which may even come from civil war times and the North turning the song around on the southerners.

Well, you could try "Union Dixie" on for size.