There is good debt and bad debt. I assume you mean high-interest credit card debt?
If there's a cash crunch right now because you're paying off debt, pat yourself on the back!!! You're doing the necessary work to get yourself to a better future.
It's OK to tell your kids there isn't a lot of money right now, unless they still believe in Santa and you've been doing Santa-driven presents. My husband was laid off when our oldest was 7, and we told him we couldn't afford much for a while. He wasn't perturbed in the least. Kids enjoy cheap activities just as much as expensive ones.
I think you can go light on presents, and give them free or affordable experiences instead. Be happy and play with them with the toys and board games they already have. Have movie night at home, with the one streaming service you haven't cut off. I suggest Netflix. Have board game night. Go to the library, read them books out loud, make all the voices, act out some scenes - my kids loved that when they were in elementary. Make meals from scratch and have them help out. I know some people will frown on this, but one New Year's Eve, we made mocktails with the kids. None of us tolerate alcohol, and we on't have any in the house, but it was something new and exciting and the kids loved it.