Brief Summary: This phase I clinical trial is studies the side effects and best dose of giving veliparib together with temozolomide in treating patients with acute leukemia. Veliparib may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as temozolomide, work in different ways to stop the growth of cancer cells, either by killing the cells or by stopping them from dividing. Giving veliparib together with temozolomide may kill more cancer cells.

Detailed Description: PRIMARY OBJECTIVES: I. To define the maximum-tolerated dose (MTD) and recommended phase II dose of ABT-888 (veliparib) administered in combination with temozolomide in patients with acute leukemias. II. To evaluate the feasibility, safety, and toxicity of administering ABT-888 in combination with temozolomide in patients with acute leukemias. SECONDARY OBJECTIVES: I. To document response in acute leukemias. II. To observe the pharmacokinetics of both ABT-888 and temozolomide when administered alone and in combination. III. To study the pharmacodynamics to determine the levels of poly(ADP-ribose) (PAR) before and after administration of ABT-888 and temozolomide in patient leukemia blasts, to analyze methyl-guanine methyl-transferase (MGMT) protein levels in primary leukemia blasts, and to quantify the induction of gamma-H2A histone family, member X (y-H2AX) and RAD51 recombinase (RAD51) foci in patient leukemia blasts after treatment. OUTLINE: This is a dose-escalation study of veliparib. Patients receive veliparib orally (PO) once daily (QD) on day 1 and twice daily on days 4-12 and temozolomide PO QD on days 3-9 of course 1. Beginning at least 30 days after the start of treatment, patients receive veliparib PO twice daily (BID) on days 1-8 and temozolomide PO QD on days 1-5. Courses repeat every 28 days in the absence of disease progression or unacceptable toxicity. Patients achieving complete remission receive 5 more courses in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up for 30 days.