Cetuximab Before Surgery in Treating Patients With Aggressive Locally Advanced Skin Cancer

Inclusion Criteria: * Patients must have untreated or relapsed SCCS that is considered to be aggressive and locally advanced by the following criteria: tumors 2 cm or more, tumors invading deep tissues such as muscle, cartilage or bone; tumors showing perineural invasion, and/or tumors metastatic to loco-regional lymph nodes; patients may have had prior surgical interventions or been treated with investigational agents with residual or recurrent disease * Patients must give informed consent * Patients must agree to pre- and post-treatment biopsies * Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Estimated life expectancy of at least 12 weeks * Negative pregnancy test Exclusion Criteria: * Second primary malignancy only if treatment would interfere with the patient's participation in this trial in the opinion of the treating physician; clear exceptions are 1) patient had a second primary malignancy but has been treated and disease free for at least 3 years, 2) in situ carcinoma (e.g. in situ carcinoma of the cervix) and, 3) additional skin cancers that have been definitively treated by surgery and/or radiation; patients with chronic lymphocytic leukemia will be allowed if their blood counts are within acceptable hematologic parameters and if they are not currently requiring cytotoxic or biologic anticancer treatment (supportive treatment such as intravenous immunoglobulin \[IVIG\] is permitted) * Patients with distant organ metastases will not be included in this study * Serious concomitant systemic disorders (including active infections) that would compromise the safety of the patient or compromise the patient's ability to complete the study, at the discretion of the investigator * History of allergic reactions attributed to compounds of similar chemical or biologic composition to cetuximab or other agents used in the study * Women who are pregnant; women of childbearing age must agree to undergo a pregnancy test prior to therapy and to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation and for 6 months after; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Serum calcium (ionized or adjusted for albumin) \< 8 mg/dl (1.75 mmol/L) or \> 12.5 mg/dl (\> 3.1 mmol/L) despite intervention to normalize levels * Magnesium \< 1.4 mg/dl (\< 0.4 mmol/L) or \> 3 mg/dl (\> 1.23 mmol/L) despite intervention to normalize levels * Potassium \< 3.5 mmol/L or \> 6 mmol/L despite intervention to normalize levels * Prior radiation therapy is not an exclusion however, patient must have documented progression at the radiation site