This phase I trial is studying the side effects and best dose of sunitinib when given together with cetuximab and radiation therapy in treating patients with locally advanced or recurrent squamous cell carcinoma of the head and neck. Sunitinib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth and by blocking blood flow to the tumor. Monoclonal antibodies, such as cetuximab, can block tumor growth in different ways. Some block the ability of tumor cells to grow and spread. Others find tumor cells and help kill them or carry tumor-killing substances to them. Radiation therapy uses high-energy x-rays to kill tumor cells. Giving sunitinib together with cetuximab and radiation therapy may kill more tumor cells.