I would NOT try Liquid Roof or similar - it is NOT intended to go directly over the wood substrate. And it will make a subsequent permanent repair more difficult.
You need to get some kind of membrane over that bare spot first. Almost any waterproof membrane will do as a temporary fix, and you can tape down the edges with a roof seam/repair tape (it doesn't have to be the Eternbond brand, though that is a superb product). Given that you are short on time, I'd try local mobile home or RV supply stores and find a suitable piece of membrane (EPDM, TPO, or what roofers sometimes call waterproofing membrane) and a roof tape. My local hardware store carries both, but there are lots of mobile homes in this area. Or you can order on Amazon or Ebay too and hopefully get prompt delivery.
You might also try to temp fix it with overlapping strips of self-adhesive flashing strips. Those are available in aluminum foil flashing or wide waterproof tapes. Multiple 6" or 8" strips should quickly fill in the damaged area. Not sure how easily it would come off again when you do the permanent fix, though.