This pilot clinical trial studies the safety of a dendritic cell vaccine when given with gemcitabine hydrochloride in treating patients with breast cancer that has spread beyond the breast and local lymph nodes to other organs in the body. The vaccine is made up of natural cells found in the blood, called dendritic cells, and peptides, or small fragments of protein which are loaded onto the dendritic cells. This combination may help activate the immune system against stromal cells, which are cells that help cancer cells survive in the body. Gemcitabine hydrochloride is a chemotherapy drug that is given before the vaccine to help shrink the tumor and control cells that may interfere with the activity of the vaccine. Interfering with the stromal cells that help support the growth of cancer cells may lead to the death of the cancer cells.