[EDIT] It turns out jwthornhill was paying a tithe to his church, paying for gym membership, cell phone service, and at least some entertainment expenses while making a child go out in the middle of the freezing cold to collect garbage to pay HIS debt. Check his blog: http://needtobedebtfree.blogspot.com/
I've never responded to posts that I've considered flamebait, and have always tried to maintain some decorum in my writings--with mixed success. I've never resorted to name calling or the use of insults or epithets without lengthy explanation, but I have to say, jwthornhill's post tests my self-control. Perhaps it's because of my own experiences when I was young that this strikes an emotional cord with me.
And so, since you came here asking for honest opinions, I'll give you mine. I find your idea thoroughly repugnant. But I want to stress that this opinion is partially based on the assumption that your debt has not been the result of excessive appeasement of your children's discretionary desires. Even if it were, even if, in the most generous case possible, you were doting but fiscally irresponsible parents who now realize that those earlier luxuries must be paid for with present hardship, your children were not told at the time of their requests that if those requests were granted, they would have to get a job to pay for them. Gifts for your children are a part of *your* finances, which are *your* responsibility and *you* have to take responsibility for them.
If you are in debt and are able to pay your debts, then pay them. If you are in debt and can't pay your debts, then you'll have to declare bankruptcy. If you are not in debt and can't pay the bills, you'll need to find some way of increasing your income(s). And, of course, you'll want to reduce your spending. Those are, as far as I know, your only options.
Regardless of what you do, however, you have a (IANAL) legal responsibility to feed, clothe, and house your children. Many people would also say that you have a moral obligation to pay, as much as is reasonable and possible, for their medical and dental expenses. If you cannot afford to pay for these things, the government provides assistance programs to help you. If you still can't afford to pay for their basic needs, then you must accept the fact that you are unable to care for your children and--I believe this can be done with minors of any age, but I'm not positive--leave them in the care of others who can, through adoption or some other service. But, what you should not do, is require people who do not enjoy full legal rights as adults to pay for their own basic needs.
And what message are you giving your children? That if they ever spend too much, or are not making enough money, they can simply send their own kids out to work minimum wage instead of investing in their own futures? Teenagers ought to be focusing their efforts on developing a valuable skillset, and their parents ought to be doing everything they can to convince them of this fact. Contrary to popular belief, performing unskilled labor as a teenager does not make one more valuable. It does not build a "work ethic that will serve them throughout their lives," to use the kind of language my critics might use. After high school, I worked as a support cook in a dingy restaurant for much less than minimum wage. I'd put in 10 hour days some days. I was expected to arrive on time, every day. My hands would bleed by the end of the shift, but no matter how hard I tried, the boss was never satisfied. Then, as a result of a miraculous windfall, I was able to stop working and went to college, where I landed a white-collar job making ~50K a year. My boss tells me I can come into work whenever I feel it, as long as I work 40 hours a week and he's happy with my performance. He's always seemed to be happy with my performance. I will retire within ten years, and I have enough free time during my work day to write this post, for example. If you force your kids to work, you sacrifice their futures for your own financial gain. I can think of nothing more despicable.
I am assuming that you are living in the United States or some roughly equivalent developed nation. If you are not, then some or all of what I have written may not apply, and I'm sorry to criticise you.