Well, of course, I could suggest not going into debt in the first place, or not spending so much, or any number of the typical suggestions, but your question was "how to pay off holiday debt quickly".
This idea comes to mind. Make January a "frugal month". By Christmas most people have partied enough, gotten new clothes, gained a little weight by eating all the holiday goodies, gotten new toys for the kids, etc. Make January a month to do without except for the bare minimum. Cook at home rather than going out (a big pot of soup or stew sounds good to me on a chilly January day), don't buy any more clothes, limit entertainment except for simple things, wear sweaters and cut the heat down a little, cut out trips, borrow DVD's rather than buying or renting them, have a "polar yard sales" with the neighbors and sell all the crap you got for Christmas that you're never going to wear or use anyway--make it fun, take a part-time job with all those places that have to do inventory, carpool, bake bread or cookies and sell them for a profit, etc. The idea would be to see just how much the family could reduce their expenses for just that month, as well as do a few things to raise a little extra cash. It might even be a fun challenge. Set a goal and see if the family could meet it (and if they do arrange some kind of reward that possibly involves time rather than money).
That's about all I've got at the moment.