Two black guys go to Ohio State University in 1933. White dudes lock horns with them. One black guy asks another what are they supposed to do, if not kicking their ass. There is the answer: "You just smile and play nice. Run every last one of these peckerwoods off their feet." I'm not sure what does the lat line mean.
to run someone off their feet means, usually, to make someone work very hard. Peckerwoods is southern slang for redneck or poor white person. Two examples I have made up.
My boss was in a really bad mood today and ran us off our feet.
I've had so much to do today and my kids have really run me off my feet.