This study will evaluate the effectiveness of the drug daclizumab for treating patients with chronic immune thrombocytopenia (ITP), a disease in which the immune system destroys platelets (blood cells involved in the clotting process). Patients with ITP have abnormal bruising and bleeding; severe disease can be life-threatening. For many patients, standard drug treatments are not effective, and many of the drugs used may have significant side effects with long-term use. Daclizumab is a genetically engineered antibody that suppresses the immune system and has been used primarily to prevent rejection in patients who have had organ transplants. Daclizumab has fewer side effects than other immune suppressant drugs.