No, it's not worth it to cash-out refinance the mortgage to pay off $4,000 in credit card debt. Bankrate's 2011 Closing Cost Survey has the national average for closing costs on a first mortgage as $4,070. You'd be paying an estimated $4,070 in expenses to change your $4,000 credit card debt at 24 percent into $4,000 in 4 percent mortgage debt.
It's also not worth it because your lender is not going to give you a cash-out refinancing on a first mortgage that's underwater. If you want to get out from under paying 24 percent on your credit card debt, start aggressively paying down the credit card balance.
That said, you may be able to refinance your underwater first mortgage through the Home Affordable Refinance Program, or HARP. You'll have to be eligible for the program, but if you're not behind on your mortgage payments and have been unable to get traditional refinancing because the value of your home has declined, you may be eligible to refinance through HARP.
These loans require a loan application and go through a loan underwriting process, and you will pay closing costs on the refinancing.
If eligible, the decision to refinance using HARP is like any other decision to refinance. Do you plan to be in the home long enough that the interest savings on the new loan exceed the refinancing costs? If refinancing makes sense, then the lower monthly payment will free up funds that you can use to pay down your credit card debt.