I'm not saying Day couldn't tap (she certainly looks like she's doing the right steps) but neither she nor Nelson are even wearing taps on their shoes. It was customary in many of the old musicals for the tap and other dance sounds to be dubbed in either before or after filming. Gene Kelly's "taps" in the "Singin' In The Rain" number were dubbed in later by Gwen Verdon, standing in a barrel of water.
