Phase II Short-term Adjuvant Therapy and Biomarker Studies With Targeted Agents in Women With Estrogen Receptor Negative Breast Cancer

Study Drug Administration: If you are found to be eligible to take part in this study, you will be randomly assigned (as in the flip of a coin) to 1 of 3 study groups: * If you are in Group 1, you will take dasatinib 40mg once a day by mouth with water. * If you are in Group 2, you will take dasatinib 80mg once a day by mouth with water. * If you are in Group 3, you will not receive dasatinib. You will be given a study drug diary to complete. In the diary, you will record when you take the study drug. Study Visits: At Month 1: * You will be called by a nurse and asked about any drugs you are taking and side effects you may be having. * You will be asked about any drugs you may be taking and side effects you may be having. * Your drug diary will be reviewed. At Month 2 you will be called by a nurse and asked about any drugs you are taking and side effects you may be having. You will also be asked to review your drug diary. This call will take about 20 minutes At Month 3 (or if you leave the study early): * You will have a fine needle aspirate (FNA) of the breast for biomarker testing. Biomarkers are found in the blood/tissue and may be related to your reaction to the study drug. * Blood (about 2-3 tablespoons) will be drawn for biomarker testing. * You will be asked about any drugs you may be taking and side effects you may be having. * Your drug diary will be reviewed. Length of Study: You may remain on study for up to 3 months. You will no longer be able to take the study drug if the disease gets worse, if intolerable side effects occur, or if you are unable to follow study directions.