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