This could be the time to get a better break from the owner/Property Manager. With December traditionally the slowest month for rentals (and sales for that matter).
To the Owner: This is a great time to offer an incentive to the prospective tenant. Let them move in December, but offer part of the month free OR a suitable Gift Card such as Sears, Home Depot, or for groceries. You will hook that respectful and open minded resident for your vacancy.
To the Renter: Don't be shy, ASK for a little break or a BONUS for moving at a time when the owner/Property Manager needs to fill a vacancy. I'm sure you will gain the respect of the owner/Property Manager and gain a welcome gift or discount.