Gefitinib in Treating Patients Who Are Undergoing Surgery and/or Radiation Therapy for Locally Advanced or Recurrent Squamous Cell Skin Cancer

Inclusion Criteria: * Within 12 weeks (+/- 2 weeks) prior to study entry, patients must have histologically or cytologically confirmed squamous cell carcinoma (SCC) of skin that is either locally advanced or recurrent with measurable disease; if the biopsy was collected outside of MDACC, the MDACC Pathology Department must assess and confirm the SCC diagnosis * Patients may have previous surgical intervention with residual or recurrent disease * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Leukocytes \>= 3,000/mm\^3 * Absolute neutrophil count \>= 1,500/mm\^3 * Platelets \>= 100,000/mm\*3 * Total bilirubin within normal institutional limits * aspartate aminotransferase (AST or SGOT) and alanine aminotransferase (ALT or SGPT) =\< 2.5 \* institutional upper limit of normal * Creatinine within normal institutional limits OR; creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Tumors must be at least 2 cms in size or have histological or cytological verification of muscle, bone, lymph node metastasis, or perineural involvement, as measured by the treating physician(s) or National principal investigator (PI) * Negative serum pregnancy test for women of child-bearing potential (performed within 14 days, +/- 1 day, prior to start of treatment); women of child-bearing potential and men must agree to use adequate contraception prior to study entry and for the duration of study partic…