Polish A Turd Meaning

(idiomatic) To work on a time-consuming and ultimately pointless or impossible task.

Example: 2006, Michael Fak, Portions of a Life: Recollections and Reflections, p. 197:
  Demaso, trying hard to scrub a wall behind one of the toilets, started complaining how dirty the walls in the entire bathroom were. Tripp also chimed in that they were polishing a turd and that what the bathroom needed was a fresh coat of paint.