Dasatinib in Treating Patients With Chronic Myelogenous Leukemia or Acute Lymphoblastic Leukemia

DISEASE CHARACTERISTICS: * Diagnosis of one of the following hematologic malignancies: * Chronic phase chronic myelogenous leukemia (CML) * In complete hematologic response after treatment on protocol UCLA-0303035, as indicated by the following criteria: * WBC ≤ upper limit of normal (ULN) * Platelet count \< 450,000/mm\^3 * No blasts or promyelocytes in peripheral blood * Less than 5% myelocytes plus metamyelocytes in peripheral blood * Peripheral blood basophils ≤ ULN * No extramedullary involvement (including no hepatomegaly or splenomegaly) * Response lasting ≥ 4 weeks after first documentation * Accelerated or blastic phase CML or acute lymphoblastic leukemia * In major hematologic response\* after treatment on protocol UCLA-0303035, defined as 1 of the following: * In complete hematologic response\*, as indicated by the following criteria: * WBC ≤ ULN * Absolute neutrophil count ≥ 1,000/mm\^3 * Platelet count ≥ 100,000/mm\^3 * No blasts or promyelocytes in peripheral blood * Bone marrow blasts ≤ 5% * Less than 5% myelocytes plus metamyelocytes in peripheral blood * Peripheral blood basophils ≤ ULN * No extramedullary involvement (including no hepatomegaly or splenomegaly) * No evidence of leukemia, as indicated by the following criteria: * WBC ≤ ULN * No blasts or promyelocytes in the peripheral blood * Bone marrow blasts ≤ 5% * Less than 5% myelocytes plus metamyelocytes in peripheral blood * Peripheral blood basophils ≤ ULN * No extramedullary involvement (including no hepatomegaly or splenomegaly) * Absolute neutrophil count ≥ 500/mm\^3 and \< 1,000/mm\^3 AND platelet count ≥ 20,000/mm\^3 and \< 100,000/mm\^3 * In minor hematologic response\* after treatment on protocol UCLA-0303035, as indicated by the following criteria: * Less than 15% in bone marrow and \< 15% in peripheral blood * Less than 30% blasts plus promyelocytes in bone marrow and \< 30% blasts plus promyelocytes in peripheral blood * Less than 20% basophils in peripheral blood * No extramedullary disease other than spleen and liver NOTE: \*Response confirmed after ≥ 4 weeks allowed provided there is no concurrent anagrelide or hydroxyurea during this time * Philadelphia chromosome-positive (Ph+) disease * Resistant or intolerant to prior imatinib mesylate * Received and benefitted from ≥ 3 months of prior therapy with dasatinib on protocol UCLA-0303035 PATIENT CHARACTERISTICS: * ECOG performance status 0-2 * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for 12 weeks after completion of study treatment * No serious uncontrolled medical disorder * No active infection that would preclude study participation * No uncontrolled angina within the past 3 months * No diagnosed or suspected congenital long QT syndrome * No history of clinically significant ventricular arrhythmias (e.g., ventricular tachycardia, ventricular fibrillation, or torsades de pointes) * QTc ≤ 450 msec on electrocardiogram * No uncontrolled hypertension * No dementia or altered mental status the would prohibit the understanding or rendering of informed consent * No history of the following significant bleeding disorders unrelated to CML: * Diagnosed congenital bleeding disorders (e.g., von Willebrand's disease) * Diagnosed acquired bleeding disorder in the past year (e.g., acquired antifactor VIII antibodies) * Not involuntarily incarcerated for either psychiatric or physical (e.g., infectious disease) illness * No patients who are imprisoned * No clinical adverse event, laboratory abnormality, or intercurrent illness that may preclude study treatment, in the opinion of the investigator * Bilirubin \< 1.5 mg/dL * ALT and AST \< 2 times upper limit of normal (ULN) * Creatinine \< 1.5 times ULN PRIOR CONCURRENT THERAPY: * See Disease Characteristics * No concurrent use of the following drugs that may confer risk of torsades de pointes: * Quinidine * Procainamide * Disopyramide * Amiodarone * Sotalol * Ibutilide * Dofetilide * Erythromycin * Clarithromycin * Chlorpromazine * Haloperidol * Mesoridazine * Thioridazine * Pimozide * Cisapride * Bepridil * Droperidol * Methadone * Arsenic * Chloroquine * Domperidone * Halofantrine * Levomethadyl * Pentamidine * Sparfloxacin * Lidoflazine * No other concurrent treatment for CML except for hydroxyurea for a 2-week duration * No concurrent medications that inhibit platelet function (e.g., aspirin, dipyridamole, epoprostenol, eptifibatide, clopidogrel, cilostazol, abciximab, ticlopidine, or any nonsteroidal anti-inflammatory drug)\* except for hydroxyurea or anagrelide * No concurrent anticoagulants (e.g., warfarin or heparin/low molecular weight heparin \[e.g., danaparoid, dalteparin, tinzaparin, or enoxaparin\]) except as prophylaxis for catheter thrombosis and/or heparin flushes for IV lines\* NOTE: \*Allowed if received previously on UCLA-0303035