ARM I, STAGE I: Patients receive autologous WT1-TCRc4 gene-transduced CD8-positive Tcm/Tn lymphocytes intravenously (IV) on days 0 and 14, cyclophosphamide IV on days 11 and 12, and aldesleukin (IL-2) subcutaneously (SC) twice daily (BID) for 14 days. Patients who have received radiation to the chest/lung tissue may receive T lymphocytes 90 days after completion of radiation.