Paclitaxel & Cyclophosphamide With or Without Trastuzumab Before Surgery in Treating Previously Untreated Breast Cancer

Inclusion Criteria: * Women with histologically proven invasive breast cancer without distant metastases; a clinical tumor classification of tumor size must be at least 1 cm with or without clinical pathologic evidence of positive nodes * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * At least one lesion that can be accurately measured in two dimensions utilizing mammogram, ultrasound, or magnetic resonance imaging (MRI) images to define specific size and validate complete clinical and pathologic response * Patients who received radiation therapy \> 5 years ago for malignancies other than breast cancer and whose radiation therapy field is not overlapping with the 20% isodose line of current radiation field are eligible, provided that radiation therapy was completed \> 5 years ago and that there is no evidence of the second malignancy at the time of study entry * Absolute neutrophil count greater than or equal to 1,500/mcl * Platelet count equal to or greater than 150,000/mcl * Alkaline phosphatase equal or less than 1.5 times the upper limit of normal (ULN) * Total bilirubin equal to or less than 1.5 times the ULN * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) no greater than 1.5 times the ULN * Creatinine less than 1.5 times the ULN * All included patients must have normal cardiac function as defined by an ejection fraction of \>= 50% and no decrease in wall motion by echocardiogram * The patient must be aware of the neoplastic nature of his/her disease and willingly provide written, informed consent after being informed of the procedure to be followed, the experimental nature of the therapy, alternatives, potential benefits, side-effects, risks, and discomforts * Women of reproductive potential must be non-pregnant and non-nursing and must agree to employ an effective barrier method of birth control throughout the study and for up to 6 months following treatment * Women of child-bearing potential must have a negative pregnancy test within 7 days of initiating study; (no childbearing potential is defined as age 55 years or older and no menses for two years or any age with surgical removal of the uterus and/or both ovaries) Exclusion Criteria: * Any patient with inflammatory breast cancer or stage IV or confirmed metastatic disease * Patients who have had any prior chemotherapy, or endocrine therapy for the treatment of breast cancer or any other cancer * Patients who cannot undergo surgery * Patients with a known or documented anaphylactic reaction or allergy to any of chemotherapy agents used in this protocol, or to antiemetics appropriate for administration in conjunction with protocol-directed therapy * Uncontrolled inter-current illness including, but not limited to ongoing or active infection requiring intravenous antibiotics, symptomatic congestive heart failure, unstable angina pectoris, or serious, uncontrolled cardiac arrhythmia, that might jeopardize the ability of the patient to receive the therapy program outlined in this protocol with reasonable safety * Patients with preexisting grade II peripheral neuropathy * Pregnant and nursing women are excluded from this study * Patients with prior malignancy will be excluded except for adequately treated basal cell or squamous cell skin cancer, adequately treated noninvasive carcinomas * Inability to cooperate with treatment protocol * Patients with known human immunodeficiency virus (HIV) infection, infectious hepatitis, type A, B or C, active hepatitis, or hepatic insufficiency * Patients may not be receiving or have received any other investigational agents during/or within 1 month prior * Any serious medical condition, laboratory abnormality, or psychiatric illness that would prevent the subject from signing the informed consent form * Myocardial infarction within 6 months prior to enrollment or has New York Heart Association (NYHA) class III or IV heart failure uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities; prior to study entry, any electrocardiogram (ECG) abnormality at screening has to be documented by the investigator as not medically relevant