This phase I/II trial studies the side effects and best dose of dasatinib when given together with cytarabine and idarubicin hydrochloride and to see how well they work in treating patients with acute myeloid leukemia that is likely to come back or spread. Dasatinib may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as cytarabine and idarubicin hydrochloride, work in different ways to stop the growth of cancer cells, either by killing the cells or by stopping them from dividing. Giving dasatinib together with cytarabine and idarubicin hydrochloride may be a better treatment for acute myeloid leukemia.