The goal of this trial is to determine the activity of erlotinib in a rationally selected population of women with ER-negative, PR-negative, HER2/neu-negative, EGFR-positive breast cancer. If erlotinib is shown to have activity, this could identify a form of targeted therapy for this specific subset of breast cancer patients. In addition, it may identify a subset of breast cancer patients with tumors that overexpress EGFR in whom other EGFR targeted therapies could warrant further testing.