SquareZ
Swing your partner, dosey-do, now clap your hands... uh-oh, that's all the square dance moves I know... I'll bluff the rest. Slap your partner in the face, Write bad checks all over the place, Flirt with strangers, annoy your spouse, Get a divorce and lose your house, ...uh... dosey-do.
--Scott Adams, writing as Dogbert
Calling Ideas for March 4, 2012

This is:

Microphone Invented
According to Those were the Days, Emile Berliner invented the telephone on March 4, 1877. I find it hard to believe that something like that was invented on a single day...but maybe so. At any rate, clearly square dancing evolved the way it has because of amplified music and the microphone; in the past, each square might have had its own caller in the square.

I don't know about any particular songs, but certainly our whole activity is dependent on the microphone.

The Second week of March is:

National Procrastination Week
Why do anything today that you can put off until tomorrow?

So if you're not prepared for the dance this week, you have a perfect excuse...

If you're willing to do ethnic stereotyping, you could do "Manana"

March is:

Optimism Month
Encourage and inspire each other to be optimistic about the future of square dancing.

Here are some songs that come to mind: