These taxes may be dischargable in bankruptcy but the amount of the debt is less than the typical fees and costs involved in a bankruptcy case. If you have other debts such as credit cards or medical bills, then it may be wise to consult with an experienced bankruptcy attorney in your jurisdiction for assistance.
The taxes might be dischargeable in bankruptcy - it will depend on the type of tax and when the returns were filed and the taxes assessed. You should consult with a bankruptcy attorney who can tell you more specific information after looking at your tax records.
As Mr. Detsky said, while these taxes may be dischargeable, the cost of doing so in the Bankruptcy is greater than the amount of the debt. You should contact the IRS or State Tax Authority and get on a payment plan. I'm going to assume this is an IRS debt. If so, under a Streamlined Fresh Start Installment Agreement, you can get into an Installment Agreement and take care of this for about $21/mo.
If you are referring to an IRS debt they only have 10 years to collect the tax from you after you file. There are certain things that will extend the 10 year time period but depending on your situation you may not have much longer before the IRS can no longer collect the tax owed.