How realistic is it to learn Liebestraum in a short amount of time?

Well, I think you should definitely go for it, but I really think maybe it would be better to give yourself more time, if that's possible. I know it's different for different people, but I learn pieces better under less pressure and no time constraints. But I think you could definitely learn it at least roughly. In that amount of time, it might be hard to really fine tune it, but... well, I think the answer is all in how well you want to learn it. My advice is to give yourself more time if possible, but I think you can do it, at least basically. Keep at the piano!