A lot depends upon the reason that you can't close by the closing date. Is this a short sale or is it just that you need to bring money to closing to be able to close? First, if you have an agent, I suggest that you discuss this fully with you agent.
If you are using the standard North Carolina "Offer to Purchase and Contract", you can fill out a amendment to the contract asking for an extension of the closing date. If the buyer agrees, you have no real problem. If this is not agreeable, read paragraph 18 at the top of page 6 of your contract. This states: "If either party is unable to close by the Closing Date, then provided that the party is acting in good faith and with resonable diligence to proceed to closing, such party shall be entitled to reasonable delay of the Closing Date and shall give as much notice as possible to the non-delaying party and closing agent. In such event, however, either party for whom the Closing Date is delayed shall have a maximum of ten (10) days from the Closing Date, or any extension of the Clsoing Date agreed-upon in writing, in which to close withou payment of interest. Following expiration of the ten-day period, the party nto ready to close shall be responsible for paying to the other party ...interest on the purchas4e price at the rate of eight percent (8%) per annum accruing from the end of the ten-day period until closing occurs or the contract is terminated. Should the delay in closing continue for mroe thatn thirty (30) days from the last agreed-upon extension of the Closing Date, however, then the non-delaying party shall have the unilateral right to terminate the contract and receive the earnest money, but the right to such receipt shall NOT affect any other remedies available to the non-delaying party for such a breach." This is where the buyer could sue your for breach of contract.
If it looks like you are going to have an extended problem, you might want to consult an attorney. I have only repeated to you what is in the Standard North Carolina REALTOR purchase contract.
Let me know if I can be of further service to you.