Abraxane and Lapatinib in Treating Patients With Stage I, Stage II, or Stage III Breast Cancer

DISEASE CHARACTERISTICS: * Histologically confirmed breast cancer * Clinical stage I-III disease * Measurable disease defined as ≥ 1 unidimensionally measurable lesion ≥ 20 mm by conventional techniques OR ≥ 10 mm with spiral CT scan * HER2/neu 3+ by immunohistochemistry or positive by fluorescent in situ hybridization * No known brain metastases * Hormone receptor status unspecified PATIENT CHARACTERISTICS: * Menopausal status not specified * Male or female * Life expectancy \> 12 weeks * ECOG performance status (PS) 0-1 OR Karnofsky PS 80-100% * WBC ≥ 3,000/mm\^3 * Absolute neutrophil count ≥ 1,500 mm\^3 * Platelet count ≥ 100,000/mm\^3 * Total bilirubin normal * AST and ALT ≤ 2.5 times upper limit of normal * Creatinine normal OR creatinine clearance ≥ 60 mL/min * LVEF ≥ 50% as measured by echocardiogram or MUGA scan * No other malignancy within the past year * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * Able to swallow and retain oral medication * No history of allergic reactions attributed to compounds of similar chemical or biologic composition to lapatinib * No ongoing or active infection * No symptomatic congestive heart failure * No unstable angina pectoris * No cardiac arrhythmia * No psychiatric illness or social situation that would preclude study compliance * No other uncontrolled illness * No gastrointestinal (GI) tract disease that would preclude ability to take oral medication * No malabsorption syndrome * No requirement for IV alimentation * No uncontrolled inflammatory GI disease (e.g., Crohn's disease or ulcerative colitis) PRIOR CONCURRENT THERAPY: * No prior chemotherapy, immunotherapy, radiotherapy, or hormonal therapy for breast cancer * No prior treatment with epidermal growth factor receptor targeting therapies * No prior surgical procedures affecting absorption * No prior surgery for breast cancer * At least 14 days since prior and no concurrent CYP3A4 inducers, including any of the following: * Dexamethasone or dexamethasone equivalent dose ≥ 1.5 mg/day, including any of the following: * Cortisone (≥ 50 mg/day) * Hydrocortisone (≥ 40 mg/day) * Prednisone (≥ 10 mg/day) * Methylprednisolone (≥ 8 mg/day) * Phenytoin * Carbamazepine * Phenobarbital * Efavirenz * Nevirapine * Rifampin * Rifabutin * Rifapentine * Hypericum perforatum (St. John's wort) * Modafinil * At least 7 days since prior and no concurrent CYP3A4 inhibitors, including any of the following: * Clarithromycin * Erythromycin * Troleandomycin * Delavirdine * Ritonavir * Indinavir * Saquinavir * Nelfinavir * Amprenavir * Lopinavir * Itraconazole * Ketoconazole * Voriconazole * Fluconazole (doses up to 150 mg/day are permitted) * Nefazodone * Fluvoxamine * Verapamil * Diltiazem * Cimetidine * Aprepitant * Grapefruit or its juice * At least 6 months since prior and no concurrent amiodarone * At least 2 days since prior and no concurrent gastric pH modifiers\*, including any of the following: * Cimetidine * Ranitidine * Nizatidine * Famotidine * Omeprazole * Esomeprazole * Rabeprazole * Pantoprazole * Lansoprazole * NOTE: \*Antacids are allowed within 1 hour before and after administration of study drug * No other concurrent investigational agents * No other concurrent anticancer therapy, including chemotherapy, radiotherapy, immunotherapy, or antitumor hormonal therapy * No concurrent herbal (alternative) medicines * No concurrent combination antiretroviral therapy for HIV-positive patients * Concurrent bisphosphonates allowed