Gemcitabine Hydrochloride and Cisplatin Before Surgery in Treating Patients With Muscle Invasive Bladder Cancer

Inclusion Criteria: * Patients must have histologically confirmed urothelial carcinoma of the bladder or urethra; patients with urothelial carcinoma of the prostatic urethra only may be included at primary investigator (PI) discretion; T-stage must be T2 to T4a; patients with radiographic N0 disease or N1 disease are eligible for the study; patients must not have radiographic evidence of metastatic disease; mixed histologies which are predominantly urothelial, such as with squamous or micropapillary differentiation, are allowed so long as there is no component of small cell histology; histology must be confirmed by a pathologist at an institution involved in this study * Patients must be candidates for radical cystectomy with the goal of cure * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin =\< institutional upper limit of normal (ULN) * Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT)(serum glutamic pyruvate transaminase \[SGPT\]) =\< 2.5 X institutional ULN * Patients must have adequate renal function defined as creatinine clearance \>= 50 mL/min; for eligibility, creatinine clearance may be either calculated using the Cockcroft-Gault formula or measured with 24 hour urine collection; note that 24 hour urine collection is required at baseline, but does not have to be used for eligibility if calculated clearance by Cockcroft-Gault is preferred; nephrostomy or ureteral stent placement in order to achieve adequate creatinine clearance is allowed * Women of child-bearing potential (WOCBP) and men with a female partner who is a WOCBP must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) starting prior to beginning treatment and continuing until at least 3 months after last dose of chemotherapy and surgery; should a woman become pregnant or suspect she is pregnant while participating in this study or if a female partner of a man participating in this study becomes pregnant, the treating physician must be notified immediately; WOCBP must have a negative serum or urine pregnancy test within 7 days prior to initiating study treatment * No other active malignancy * Ability to understand and the willingness to sign written informed consent and Health Insurance Portability and Accountability Act (HIPAA) documents Exclusion Criteria: * Patients who have had intravesicular therapy within 4 weeks of study entry, or those who have not recovered from adverse effects of such agents administered more than 4 weeks earlier * Patients may not be receiving any investigational agents within 4 weeks of study entry * History of allergic reactions attributed to compounds of similar chemical or biologic composition to gemcitabine or cisplatin or other agents used in the study * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study * Known human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible * Patients who have undergone prior radiation to greater than or equal to 25% of the bone marrow within the past year are excluded * Patients who have received any previous systemic chemotherapy or radiation therapy for urothelial carcinoma within 1 year of study entry are ineligible