This is a phase II study designed to study the effectiveness of combined radiotherapy and erlotinib in the postoperative setting for patients with cutaneous SCC that are at high risk for recurrence. Participants enrolled in the study will be evaluated by a head and neck surgeon, and a radiation oncologist. Whenever possible, a preoperative biopsy will be performed after participant enrollment in the study for histological confirmation and for molecular correlates. Participants enrolled prior to surgical resection will begin erlotinib at 150 mg by mouth (PO) every day (QD) (14 tablets) to be taken 14 days prior to surgical resection. Following planned surgical resection, the participant will begin Erlotinib therapy and radiotherapy at the same time and within 4-8 weeks of the surgical resection.