Erlotinib Hydrochloride in Treating Participants With Muscle Invasive or Recurrent Urothelial Cancer

Inclusion Criteria: * Patients must have histologic proof of urothelial cancer. This includes bladder cancer, in addition to other tumors of the urothelial lining including renal pelvis, ureteral, and urethral cancer. This group may include any patient requiring cystectomy, including patients with recurrent or extensive superficial disease (cTa-T1N0M0), CIS (carcinoma in situ), or muscle invasive disease (cT2-3aN0M0), whose tumor could not be completely removed at transurethral resection * Patients with the following high-risk features: Micropapillary features (more than focal on pathology); Small cell carcinoma; 3-dimensional (D) mass on exam under anesthesia (EUA); Lymphovascular invasion; Hydronephrosis (unless in the opinion of the treating physician, this is not due to tumor); High grade (grade 3) tumors of the ureter, renal pelvis, or urethra, or tumors in these areas with radiographic abnormality large enough to recognize as an abnormal mass by computed tomography (CT) or magnetic resonance imaging (MRI) imaging; Direct invasion of the prostatic stroma or the vaginal wall (ie: cT4a disease) should be offered neoadjuvant cytoreductive chemotherapy (ie: cisplatin-based). Patients refusing or who are not considered candidates for cytoreductive chemotherapy may be considered eligible. Dr. Siefker-Radtke will be the final arbiter in determining eligibility for the trial * Please note that the presence of variant histologic subtypes is acceptable, except in the case for small cell variant which is traditionally treated with cytoreductive chemotherapy. Patients with small cell who refuse recommended cytoreductive chemotherapy may still be considered eligible * Patients must have an evaluation in the department of urology, and be deemed an acceptable surgical candidate * Patients must NOT have clinical evidence of metastatic disease by either CT or MRI of the abdomen and pelvis, and chest x-ray. In the absence of a bone scan, patients should be free of bone pain and have an alkaline phosphatase \< 1.5 x upper limit of normal (ULN) of the upper limit of normal, or a normal bone fraction of alkaline phosphatase. If these features are present, patients should have a bone scan and this should be interpreted as showing no evidence of metastatic disease in order to be eligible * Patients, 18 years and older, must either be not of child bearing potential or have a negative pregnancy test within 2 weeks of treatment. Patients are considered not of child bearing potential if they are surgically sterile (they have undergone a hysterectomy, bilateral tubal ligation, or bilateral oophorectomy) or they are postmenopausal * Absolute neutrophil count (ANC) \>= 1,000/ul * Platelets \>= 75,000/microliters * Creatinine =\< 2.0 x institutional upper limit of normal (ULN), or a creatinine clearance of \> 30 ml/min as calculated by Cockroft-Gault or by 24-hour urine collection * Bilirubin =\< 2.5 x ULN * Aspartate aminotransferase (AST) =\< 5.0 x ULN * Zubrod performance status (PS) =\< 2 * Patients with second malignancies are eligible provided that the expected outcome from the second cancer is such that this will not interfere in the delivery of this therapy, or in doing cystectomy, and provided that the expectation of survival from any prior malignancy is reliably \> 4 years Exclusion Criteria: * Acute hepatitis or known human immunodeficiency virus (HIV) * Active or uncontrolled infection * Significant history of uncontrolled cardiac disease; i.e., uncontrolled hypertension, unstable angina, recent myocardial infarction (within prior 6 months), uncontrolled congestive heart failure, and cardiomyopathy with decreased ejection fraction =\< 40% * Prior therapy specifically and directly targeting the EGFR pathway * Patients with interstitial lung disease * Any concurrent chemotherapy not indicated in the study protocol or any other investigational agent(s) * Patients with metastatic or surgically unresectable disease are not eligible for this study. In addition, patients who do not agree to surgery are not eligible for this trial * Patients who have received prior systemic chemotherapy or radiation therapy for urothelial cancer are not eligible. Any prior intravesical chemotherapy is allowed