The purpose of this study is to find the highest dose of dasatinib that can be safely given to a patient when the drug is given in combination with the known anticancer drug paclitaxel. Paclitaxel is an established anti-cancer drug, used in the treatment of many cancers, and it is an approved treatment for breast cancer. Dasatinib has been approved by the Food and Drug Administration for use as a single therapy in another kind of cancer, but its use in breast cancer patients, and in combination with paclitaxel is investigational.