Don't short-change him now. My son goes to a Jewish day school and so has double the workload of many children his age. My problem is he does not want to do his homework. I feel like we are engaged in battle. I encourage, push, prod, threaten and punish.
Nothing seems to work.
Try doing nothing at all. Your tuition pays for your son to have a full-time teacher whose job it is to assign homework and to make sure it gets done. If he is not getting his work done, that is between him and the teacher who assigned it. And there is no better way to teach this particular lesson then to send your son to school unprepared. If he is not taught now that he is responsible for getting his own work done, the battle you are currently engaged in will turn into an all-out war when your son gets older.