You should call them and inform them that if you do not have it in 24 hours, you will fill an official complaint with the state AG. By law the county has 90 days to either issue you a permit or deny you.
§ 14‑415.15. Issuance or denial of permit.
(a) Except as permitted under subsection (b) of this section, within 90 days after receipt of the items listed in G.S. 14‑415.13 from an applicant, the sheriff shall either issue or deny the permit. The sheriff may conduct any investigation necessary to determine the qualification or competency of the person applying for the permit, including record checks.
(b) Upon presentment to the sheriff of the items required under G.S. 14‑415.13 (a)(1), (2), and (3), the sheriff may issue a temporary permit for a period not to exceed 90 days to a person who the sheriff reasonably believes is in an emergency situation that may constitute a risk of safety to the person, the person's family or property. The applicant may submit proof of a protective order issued under G.S. 50B‑3 for the protection of the applicant as evidence of an emergency situation. The temporary permit may not be renewed and may be revoked by the sheriff without a hearing.
(c) A person's application for a permit shall be denied only if the applicant fails to qualify under the criteria listed in this Article. If the sheriff denies the application for a permit, the sheriff shall, within 90 days, notify the applicant in writing, stating the grounds for denial. An applicant may appeal the denial, revocation, or nonrenewal of a permit by petitioning a district court judge of the district in which the application was filed. The determination by the court, on appeal, shall be upon the facts, the law, and the reasonableness of the sheriff's refusal. The determination by the court shall be final. (1995, c. 398, s. 1; 2005‑343, s. 1.)