SJG-136 in Treating Patients With Relapsed or Refractory Acute Leukemia, Myelodysplastic Syndromes, Blastic Phase Chronic Myelogenous Leukemia, or Chronic Lymphocytic Leukemia

Inclusion Criteria: * Diagnosis of 1 of the following hematologic malignancies: * Acute myeloid leukemia * Acute lymphoblastic leukemia * Myelodysplastic syndromes * Chronic myelogenous leukemia in blastic phase * Chronic lymphocytic leukemia * Relapsed or refractory disease * No immediately available, potentially curable options (e.g., stem cell transplantation) available * Bilirubin normal (unless elevated due to Gilbert's syndrome) * HIV positivity allowed provided CD4 counts are normal with no AIDS-defining disease * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No uncontrolled intercurrent illness including, but not limited to, any of the following: * Ongoing or active infection * Symptomatic congestive heart failure * Unstable angina pectoris * Cardiac arrhythmia * Psychiatric illness or social situations that would limit study compliance * Recovered from prior therapy * ECOG performance status =\< 2 * SGOT and SGPT =\< 2.5 times upper limit of normal (ULN) * Creatinine normal OR creatinine clearance \>= 60 mL/min * Primary resistance (i.e., failed to achieve a complete remission \[CR\] to a standard induction regimen) or relapsed after achievement of a CR. * Must have documented failure to last cytotoxic regimen prior to study entry. * Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * No known CNS disease * No history of allergic reactions attributed to compounds of similar chemical or biologic composition to SJG-136 * More than 7 days since radiotherapy * No concurrent combination antiretroviral therapy for HIV-positive patients * No other anti-leukemia agents except hydroxyurea =\< 5 grams/day =\< 14 days prior to and during first course of treatment to control blood counts