This year, I discovered a great way to fill an activity for the day that doesn't take a lot of time, and can accommodate any number of people, so you can keep it in reserve for when you have to adjust your original plans.
It is a game called Pass the Parcel. All you need is a prize, (preferably something everyone can enjoy together so there is no winner and loser at the end, thus avoiding hurt feelings) wrapping supplies, and a dice. You can even call this a 'learning game' if you wanted, since it involves number recognition. Ideas for group prizes: a new Christmas video for the family, a box of treats, a new book to read together, a package of finger puppets, a puzzle to build, supplies for a craft, etc.
Step 1: Wrap your prize in layer upon layer upon layer of paper. I think I used ten this year. (You can do this in advance and tuck the prize under your bed until that busy day creeps up on you. Then you are prepared!)
Step 2: Get all the participants into a circle.
Step 3: Roll the dice. If the player rolls a predetermined number (we used 3, but it is just whatever you pick) they get to start unwrap the gift.
Step 5: When someone else gets the lucky number, they get the gift and start unwrapping as fast as they can.
Step 6: Keep rolling the dice, and passing the parcel accordingly, until all the wrappings are gone.