don't spend the entire IRA on debt, or you won't have any money to pay the income tax at tax time.

False ... any IRA distribution you take is taxable to you  no matter what you use the money for...however there is no 10% penalty on inherited IRAs.   Before you do anything you may want to seek guidance from a local attorney as you may not need to pay off the debt. 

Totally agree.  Unless you co-signed for the debt, his Estate (not you personally) is responsible for the debt.  But who was retirement plan beneficiary?  His Estate or you personally?