This is:

Public Sleeping Day

Hmmm...certainly not an activity you want to encourage at a square dance. However, you could do The Lovin' Spoonful's Daydream, and there's a song called "Don't Wake Me Up"

Mairzy Doats was #1

Recorded by the Merry Macs, and written by Jerry Livingston.

There's a singing call version of this silly ditty; I usually use it for patter.