GTI-2040 in Treating Patients With Relapsed, Refractory, or High-Risk Acute Leukemia, High-Grade Myelodysplastic Syndromes, or Refractory or Blastic Phase Chronic Myelogenous Leukemia

Inclusion Criteria: * Diagnosis of 1 of the following: * Acute myeloid leukemia (AML) or acute lymphoblastic leukemia (ALL) refractory to primary standard induction therapy * Relapsed or refractory acute leukemia * Chronic myelogenous leukemia (CML) in blast crisis at diagnosis OR that failed prior aggressive induction chemotherapy * Diagnosis of 1 of the following: * Acute leukemia secondary to preexisting hematologic condition or prior chemotherapy at diagnosis OR that failed prior aggressive induction chemotherapy * Advanced myelodysplastic syndromes (intermediate-1 or greater) * De novo acute leukemia (myeloid or nonmyeloid) * Not a candidate for aggressive standard induction chemotherapy * De novo AML or ALL (patients \> 60 years of age) * No suspected or proven active CNS leukemia * ECOG performance status (PS) 0-2 OR Karnofsky PS 50-100% * Life expectancy \>= 8 weeks * Bilirubin =\< 1.5 mg/dL * AST and ALT \< 3 times upper limit of normal (ULN) * Creatinine =\< 1.5 times ULN * No HIV positivity * Fertile patients must use effective contraception * No history of allergic reactions attributed to other phosphorothiolated oligonucleotides * No uncontrolled intercurrent illness including, but not limited to, any of the following: * Ongoing, active, or poorly controlled infection * Symptomatic congestive heart failure * Unstable angina pectoris * No uncontrolled intercurrent illness including, but not limited to, any of the following: * Cardiac arrhythmia * Poorly controlled pulmonary disease * Psychiatric illness or social situation that would preclude study compliance * Recovered from all prior therapies * Prior autologous or allogeneic stem cell transplantation allowed (No active graft-vs-host disease \> grade 2) * At least 2 weeks since prior and no concurrent cytotoxic chemotherapy * At least 2 weeks since prior and no concurrent biologic therapy * At least 2 weeks since any other prior investigational agent * No other concurrent anticancer therapy, including radiotherapy or hormonal therapy * Concurrent imatinib mesylate for CML allowed * Not pregnant or nursing * Negative pregancy test