Combination Chemotherapy and Paclitaxel Plus Trastuzumab in Treating Women With Palpable Breast Cancer That Can Be Removed by Surgery

Inclusion Criteria: * Diagnosis of invasive adenocarcinoma by core needle biopsy * Fine needle aspiration allowed provided primary tumor size \< 2 cm and lymph node metastases are present * Excisional biopsy of the primary tumor allowed provided biopsy-positive lymph nodes are present * Primary tumor ≥ 2 cm and/or ≥ 1 biopsy-positive lymph node * HER2-positive disease * Confirmation by fluorescent in situ hybridization (FISH) requires gene amplification * Confirmation by immunohistochemistry (IHC) requires a strongly positive (3+) staining intensity score * Ductal carcinoma in situ (DCIS) or synchronous DCIS of the contralateral breast regardless of prior therapy allowed * Synchronous invasive breast cancer not allowed * Ipsilateral DCIS treated by local excision with or without hormonal therapy allowed * Those treated with radiation therapy are not allowed * No definitive clinical or radiologic evidence of metastatic disease * No history of invasive breast cancer * Hormone receptor status known * Menopausal status not specified * ECOG performance status of 0 -1 * Absolute neutrophil count ≥ 1,200/mm³ * Platelet count ≥ 100,000/mm³ * Total bilirubin normal unless the patient has a grade 1 bilirubin elevation (normal to 1.5 times upper limit of normal \[ULN\]) resulting from Gilbert disease or similar syndrome due to slow conjugation of bilirubin * Alkaline phosphatase ≤ 2.5 times ULN * AST ≤ 1.5 times ULN * Creatinine normal * Left ventricular ejection fraction (LVEF) ≥ 55 by multi gated acquisition scan (MUGA) or echocardiogram (ECHO) within the past 3 months * Patients with either skeletal pain or alkaline phosphatase that is \> ULN but ≤ 2.5 times ULN allowed if bone scans fail to demonstrate metastatic disease * Suspicious findings on bone scan must be confirmed as benign by x-ray, MRI, or biopsy * Prior non-breast malignancies allowed if disease-free for 5 years since completion of initial treatment regimen and deemed by their physician to be at low risk for recurrence * Patients who had the following cancers are eligible if diagnosed and treated within the past 5 years: * Carcinoma in situ of the cervix * Colon carcinoma in situ * Melanoma in situ * Basal cell and squamous cell carcinoma of the skin * No cardiac disease that would preclude the use of epirubicin hydrochloride or trastuzumab (Herceptin®) including any of the following: * Active cardiac disease * Angina pectoris that requires the use of antianginal medication * Cardiac arrhythmia requiring medication * Severe conduction abnormality * Clinically significant valvular disease * Cardiomegaly on chest x-ray * Ventricular hypertrophy on EKG * Patient's with poorly controlled hypertension ( i.e., diastolic greater than 100 mm/Hg) * Patients with hypertension that is well controlled on medication are eligible * History of cardiac disease * Myocardial infarction documented as a clinical diagnosis or by EKG or any other tests * Documented congestive heart failure * Documented cardiomyopathy * No sensory or motor neuropathy ≥ grade 2, as defined by the NCI's CTCAE v3.0 * Women of reproductive potential must agree to use an effective non-hormonal method of contraception during therapy * Women of child bearing potential must have a negative urine or serum pregnancy test within 2 weeks of registration * Not pregnant or nursing * No psychiatric or addictive disorders or other conditions that, in the opinion of the investigator, would preclude the patient from meeting the study requirements * No non-malignant systemic disease (e.g., cardiovascular, renal, hepatic) that would preclude treatment with either of the treatment regimens * No prior surgical axillary staging procedure * Prior non-excisional biopsy of an axillary node allowed * No prior treatment for this breast cancer * Hormonal therapy allowed if had been given for up to a total of 28 days anytime after diagnosis and before study entry * Hormonal therapy must stop at or before study entry and be re-started, if indicated, following surgery * No prior therapy with anthracyclines or taxanes for any malignancy * No other investigational agents within the past 30 days * No concurrent sex hormonal therapy (e.g., birth control pills, ovarian hormonal replacement therapy) * No concurrent therapy with any hormonal agent such as raloxifene, tamoxifen, or other selective estrogen receptor modulator (SERM), either for osteoporosis or breast cancer prevention