Gotta love it when someone does the math for you. From Tara Siegel Bernard's NY Times article published May 15, 2009, "Weighing the Options With Credit Card Debt:"

...if you carry $10,000 on a credit card with an 18 percent rate and make only the minimum payment (say, 1 percent of the balance plus interest), it will take 32 years to pay it off — for a grand total of $24,834. That does not count late fees or over-the-limit charges.

Note that generally in absence of fraud or other bad faith relating to the incurrence of debt, this attorney is able to discharge that debt for less than 1/24 of the amount and in less than 1/120 of the time (a chapter 7 takes 3 months) it'd take to pay off the debt to the creditor.

After listing caveats about debt negotiation and settlement, the Times writer concludes with a discussion of bankruptcy:

...For some people, at least, it pays to visit a bankruptcy lawyer, where the initial consultations should be free. A lawyer can advise you of your rights and walk you through the many implications of bankruptcy. “It’s not a bad idea if you’re under a lot of financial stress or you are afraid of losing your assets,” Ms. Detweiler said. It also pays to meet with a bankruptcy lawyer and a credit counselor before you consider debt settlement. “If you do it the other way around, you are very vulnerable to being led down the wrong path,” she said. “And what I find is that people hear what they want to hear.”