The same thing happened to me. The delivery guys showed up with most of my furniture, but not my dresser. It took a whole lot of phone calls to find out wtf happened. No one could tell me when I was getting the dresser. I think I had to wait a month, but it came. And I still had to pay full price, and nothing was refunded. But I was certainly peeved that no one said upfront that any of that was going to happen.
I would just wait for the furniture and file away the experience as something you'll know to ask about next time.