Combination Chemotherapy and Dasatinib in Treating Participants With Philadelphia Positive or BCR-ABL Positive Acute Lymphoblastic Leukemia.

Inclusion Criteria: * Diagnosis of one of the following: Previously untreated Ph-positive acute lymphoblastic leukemia (ALL) (either t(9;22) and/or BCR-ABL positive) (includes patients initiated on first course of hyper-CVAD before cytogenetics known). These groups will be analyzed separately. After 1-2 courses of chemotherapy with or without imatinib mesylate (Gleevec). If they achieved complete response (CR), they are assessable only for event-free and overall survival, or if they failed to achieve CR, they are assessable for CR, event-free, and overall survival. Patients with relapsed Ph-positive ALL or lymphoid blast phase of chronic myelogenous leukemia (CML) * Eastern Cooperative Oncology Group (ECOG) performance status less than or equal to 2 * Adequate liver function (bilirubin less than or equal to 3.0 mg/dl, unless considered due to tumor), and renal function (creatinine less than or equal to 3.0 mg/dl, unless considered due to tumor) * Adequate cardiac function as assessed clinically * Signed informed consent Exclusion Criteria: * Active serious infection not controlled by oral or intravenous antibiotics * Treatment with any investigational antileukemic agents or chemotherapy agents in the last 7 days before study entry, unless full recovery from side effects has occurred or patient has rapidly progressive disease judged to be life-threatening by the investigator * Active secondary malignancy other than skin cancer (e.g., basal cell carcinoma or squamous cell ca…