This phase II trial is studying how well giving bevacizumab together with interleukin-2 works in treating patients with metastatic kidney cancer. Monoclonal antibodies, such as bevacizumab, 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. Bevacizumab may also stop the growth of tumor cells by blocking blood flow to the tumor. Interleukin-2 may stimulate the white blood cells to kill tumor cells. Giving bevacizumab together with interleukin-2 may kill more tumor cells.