Vaccine Therapy With or Without Interleukin-2 After Chemotherapy and an Autologous White Blood Cell Infusion in Treating Patients With Metastatic Melanoma

Inclusion Criteria: * Diagnosis of metastatic melanoma * No tumor reactive cells available for cell transfer therapy * Measurable disease * Previously treated with interleukin-2 (IL-2) and meets 1 of the following criteria: * No response (progressive disease) * Recurrent disease * HLA\*0201 positive * ECOG performance status 0 or 1 * Absolute neutrophil count \> 1,000/mm\^3 * Platelet count \> 100,000/mm\^3 * Hemoglobin \> 8.0 g/dL * ALT and AST \< 3 times upper limit of normal * Bilirubin ≤ 2.0 mg/dL (\< 3.0 mg/dL if Gilbert's disease is present) * Creatinine ≤ 2.0 mg/dL * Life expectancy ≥ 3 months * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for up to 4 months after receiving the preparative regimen * No active systemic infections, coagulation disorders, or other major medical illnesses of the cardiovascular, respiratory, or immune system, as evidenced by a positive stress thallium or comparable test, myocardial infarction, cardiac arrhythmias, or obstructive or restrictive pulmonary disease * No autoimmune disease (e.g., autoimmune colitis or Crohn's disease) or primary immunodeficiency disease * No HIV positivity * No hepatitis B or C virus positivity * No Epstein-Barr virus negativity * Eligible to receive high-dose IL-2, as evidenced by the following: * Patients ≥ 50 years of age must have a normal cardiac stress test (e.g., stress thallium, stress MUGA, dobutamine echocardiogram, or othe…