This phase I trial studies the side effects and best dose of veliparib when given together with cisplatin and vinorelbine ditartrate in treating patients with breast cancer that has returned or spread to other parts of the body. Veliparib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as cisplatin and vinorelbine ditartrate, 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. Giving veliparib together with combination chemotherapy may be a better treatment for breast cancer.