I've had success with putting a cup of baking soda into the disposal, on top of the standing water, then pouring about 2 cups vinegar. It will foam up. Let it sit for about 30 minutes, then run the disposal and flush with water. It breaks up the clog and has worked for me several times.

I understand that onion skins are notorious for clogging up the sink disposal. I have heard that Plumbers always have a lot of business around Thanksgiving.