Hmmm, I agree with Sherieb...if you're there for three weeks then it's definately worth lugging your mattress accross. If this is too hard, then I suggest the floor (unless it's concrete or something!Surely a straight back is better than a wonky one?!!
Or turn the mattress...maybe it's never been turned and the other side is AWESOME!!! Probaby not though, eh? Can you take the cushions off the couch and sleep on them?
Sleep well my friend!