I strongly recommend that you speak to a probate attorney. I will say that unless you personally agree to be liable for the debts, you will not be personally liable for any of them. Any assets of the estate may be required to pay the debts before you can inherit.
This is an interesting question and a bit difficult to answer. Did your mother leave a will? Are you her only child? Are there other assets in the estate?
The reason I ask, is that in NC, the real estate becomes the property of the heirs upon death,. While you are not responsible for your mother's debts, the creditors are entitled to be paid and have the right to go after your mother's assets, including the home. If you and the other heirs don't want the house and can't pay the mortgage and dont' want to refinance, it would probably be best to contact the creditors so that they can start doing what they need to do. This would limit future liability for rent, taxes and liability associated with the home.
I agree with the other attorneys' answers. If you, or none of the other heirs, are interested in keeping the house, you don't have to. However, creditors, including the mortgage holder, are entitled to compensation if there are any assets in the estate. You should consider consulting with a probate attorney to discuss your options going forward.