This study will examine a new approach to treating patients with severe systemic lupus erythematosus (SLE) that involves collecting stem cells (cells produced by the bone marrow that develop into blood cells) from the patient, completely shutting down the patient's immune system, and then giving back the patient's stem cells. SLE is a chronic, inflammatory disorder of the immune system that can affect many organs. It is called an autoimmune disease because the patient's lymphocytes (white blood cells that normally protect against invading organisms), go out of control and attack the body's own tissues.