Patients receive preconditioning chemotherapy comprising fludarabine phosphate IV over 15 minutes on days -5 to -1 or cyclophosphamide IV over 1 hour on days -7 to -6 and fludarabine phosphate IV over 15 minutes on days -5 to -1. They receive MFE23 scFv-expressing autologous anti-CEA MFEz T lymphocytes IV over 30 minutes on day 0. Patients also receive high-dose aldesleukin IV over 15 minutes every 8 hours for up to 12 doses beginning on day 0, in the absence of disease progression or unacceptable toxicity. If there is evidence of MFE23 scFv-expressing autologous anti-CEA MFEz T lymphocytes survival, patients may receive additional high-dose aldesleukin.