If you are able to get a credit card company to discharge all or part of your debt. Then don't be surprised to see a tax statement sent to you and the IRS for the amount that was forgiven.
The IRS sees that as a taxable event and the debtor recognizes gross income equal to the amount of the debt cancelled.
Note, if this debt was discharged via a bankruptcy then a taxable event did not occur and you will not be taxed on that amount.