This randomized phase II trial studies how well veliparib works with combination chemotherapy and radiation therapy in treating patients with rectal cancer that has spread from where it started to nearby tissue or lymph nodes (locally advanced). Veliparib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as modified (m)FOLFOX6 regimen, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Radiation therapy uses high-energy x-rays to kill tumor cells and shrink tumors. Giving veliparib with combination chemotherapy and radiation therapy may kill more tumor cells and giving it before surgery may make the tumor smaller and reduce the amount of normal tissue that needs to be removed.