Sirolimus, Cisplatin, and Gemcitabine Hydrochloride in Treating Patients With Bladder Cancer

Inclusion Criteria: * Signed informed consent form (ICF) providing agreement to adhere to the dosing schedule, report for all trial visits and authorization, use and release of health and research trial information * Histologically or cytologically confirmed carcinoma of the bladder of all histologies except neuroendocrine differentiation or squamous cell histology * Eastern Cooperative Oncology Group (ECOG) performance status of =\< 1 * Eligibility for phase 1 and phase 2 components: * Phase 1 - clinical T3 or T4 or N1 or M1 cancer which is untreated or previously treated with platinum based therapy with primary tumor still present in the bladder and amenable to sampling before and after treatment, as indicated * Phase 2 - clinical T2-4 N0 or N1 untreated with primary tumor still present in the bladder and amenable to sampling before and after treatment, as indicated * Life expectancy \>= 12 weeks * No prior malignancy is allowed except: * Adequately treated basal cell or squamous cell skin cancer or * In situ carcinoma of any site or * Other adequately treated malignancy for which the patient is currently disease free for at least one year * Absolute neutrophil count \>= 1.5 x 10\^9 cells/L * Hemoglobin (Hgb) \>= 9.0 g/dL * Platelets \>= 100,000 x 10\^9/L * Aspartate aminotransferase (AST), alanine aminotransferase (ALT) =\< 1.5 x upper limit of normal (ULN) * Bilirubin and total bilirubin levels =\< 1.5 x ULN * Serum creatinine \< 1.5 X institutional ULN mg/dL OR glomerular filtration rate (GFR) \>= 50 mL/min * All pre-study labs required for determination of eligibility are to be completed within 30 days prior to day -2 (or the next business day if falls on a weekend or holiday) * X-rays and/or scans to assess all disease sites are to be completed within 30 days prior to day -2 (or the next business day if falls on a weekend or holiday) Exclusion Criteria: * Patients currently receiving active therapy for other neoplastic disorders * Known parenchymal brain metastasis * Active or symptomatic viral hepatitis or chronic liver disease * Clinically significant heart disease as evidenced by myocardial infarction, or arterial thrombotic events in the past 6 months, severe or unstable angina, or New York Heart Association (NYHA) class II-IV heart disease or cardiac ejection fraction measurement of \< 45 % at baseline, if done * Atrial fibrillation, or other cardiac arrhythmia requiring medical therapy * Administration of an investigational therapeutic within 30 days of cycle 1, day 1 * Patients with dementia/psychiatric illness/social situations that would limit compliance with study requirements or would prohibit the understanding and/or giving of informed consent * Patients with medical conditions, which, in the opinion of the investigators, would jeopardize either the patient or the integrity of the data obtained will not be eligible * Any condition which, in the opinion of the investigator, would preclude participation in this trial