Thanks for the suggestions. The trap is clear and boiling water didn't help. I can't snake it myself, but I think I can get someone to come out this afternoon to do that. I just really don't want to have to call a plumber for this! The reason I wanted to do the baking soda/vinegar thing is because I have always had better luck with it than the harsh chemicals. I guess because I don't worry too much about having to do it several times, but the Liquid Plum'r I'm afraid will eat through our 60 year old pipes if I have to use it more than once. Ick ick ick. Thanks again!
ETA: Next time I'm at a store that sells them, I am definitely picking up a couple of those Zip it things. I hadn't heard of them before but they look like something I can use, at least if the clog is close to the opening.