How new does it have to be? Could I use a game that's been in development for a while but isn't finished yet? Even if demos or such have already been published?
We're going by the honor system here, and I'm not going to strictly define what a "new" game is. After hosting a bunch of jams in the past, I find that most game jam entries, including the winners, tend to be completed in the span of a week or two.
If hassled, I'd say that a game whose content is beyond "half done" is stretching it. So it's OK if you have a demo with just the base mechanics finished, but not OK if you submit a 60 level game where you've already completed 30 levels.