The most important gift you can give your children is to instill the need to live within your means, save for the future and that happiness isn't some junk bought from the store that is quickly forgotten.
This is not a we won't have Christmas this year, but have it on a very strict budget. If there is just no money between now and Christmas to be had, you can't afford to pay back what you borrow either.
Then for next year, you start the family on a Christmas savings plan. Have everyone make contributions, things like pocket change, and so on. Keep track of accounts and such. Then next year you give each child everything they've saved plus a portion of what the family has saved (that would mean the parents) with one thing. Not over half the total can come in the last three months of the year.
Many if not most people go through life moving and reacting only to the closest crises, never getting ahead, never ready for even the predictable things. If you use this event to teach your children how to get off the crises treadmill, plan for their future and live within their means, you will materially improve their lives and satisfaction with life. What a wonderful gift.