I cannot get the plastic washer to loosen to remove the ballccock. Any suggestions?

Take the ball and ball arm off the ballcock and then hold the nut with a pair of pliers and then spin the entire ballcock assembly with your other hand (or pair of pliers) to remove the unit.

Otherwise, if that doesn't work you can take a hacksaw blade and simply cut the plastic nut off... ;)

Mark

Another option would be to take a chisel and hammer and start the nu. Turning counterclockwise. All good solutions, what's your pleasure? Good luck, Tom