Vorinostat and Idarubicin in Treating Patients With Relapsed or Refractory Leukemia or Myelodysplastic Syndromes

Inclusion Criteria: * Patients must have histologically or cytologically confirmed relapsed/refractory acute myelogenous leukemia, acute lymphocytic leukemia, myelodysplastic syndrome or blastic phase chronic myelogenous leukemia. * Patients that have received cumulative doses (or its equivalent to other anthracycline) of more than 290 mg/m\^2 of idarubicin will be excluded from the study. No other limitations in terms of number of prior therapies or type of therapies apply to this study. * ECOG performance status (PS) 0-2 OR Karnofsky PS 60-100% * Total bilirubin ≤ 2 mg/dL * AST and ALT ≤ 2.5 times upper limit of normal * Creatinine ≤ 2 mg/dL * LVEF ≥ 50% * Not nursing or pregnant * Negative pregnancy test * Fertile patients must use effective contraception * At least 2 weeks since prior chemotherapy and recovered, unless there is evidence of rapidly progressive disease, at least 24 hours since prior hydroxyurea for rapidly proliferating disease * At least 2 weeks since prior imatinib mesylate * At least 2 weeks since prior histone deacetylase inhibitors, including valproic acid * Maximum cumulative dose of prior idarubicin or equivalent anthracycline drug ≤ 290 mg/m2 * No concurrent epoetin alfa or hematopoietic colony-stimulating factors during the first course of study therapy * No concurrent prophylactic hematopoietic colony-stimulating factors * Myelodysplastic syndromes requiring treatment, previously treated with either azacytidine or decitabine, unless it was contraindicated; blastic phase chronic myelogenous leukemia; failed prior imatinib mesylate-based therapy * Patients with MDS should have received therapy with either 5-azacytidine or 5-aza-2'-deoxycytidine, unless the patient had a contraindication to such therapy, and should require therapy. * Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * Patients with clinical evidence of CNS disease should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. * No unstable angina pectoris * Considered ineligible for or refused potentially curative therapy, including allogeneic stem cell transplantation, with or without standard induction therapy * No history of allergic reaction attributed to compounds of similar chemical or biological composition to vorinostat (SAHA) or other agents used in this study * No ongoing or active infection * No symptomatic congestive heart failure * No cardiac arrhythmia * No other uncontrolled illness * No psychiatric illness or social situation that would preclude study compliance * No other concurrent investigational agents * No other concurrent anticancer agents or therapies * No concurrent combination antiretroviral therapy for HIV-positive patients