Capecitabine, Oxaliplatin, and Radiation Therapy in Treating Patients Who Are Undergoing Surgery for Stage I Rectal Cancer

Inclusion criteria

* Patient must have an Eastern Cooperative Oncology Group (ECOG)/Zubrod status of =\< 2 * Patient must have histologically confirmed invasive adenocarcinoma of the rectum; Note: patients with rectal tumors suspicious for invasion also are eligible * Distal border of the patient's tumor must be within 8 cm from the anal verge as measured on endoscopic exam * Patients with tumors fixed to adjacent structures on digital exam are NOT eligible * Patient must have an uT2uN0 tumor, as confirmed by endorectal ultrasound (ERUS) or endorectal coil magnetic resonance imaging (MRI) scan; patients with uT1, uT3, or uT4 tumors are NOT eligible; greatest diameter of tumor cannot exceed 4 cm * Patients with positive perirectal nodes on ERUS examination are NOT eligible * Patients with histologic evidence of metastatic invasion of inguinal lymph nodes are NOT eligible * Patients with the following conditions are NOT allowed on study: * Metastatic disease or other primaries (patient must have had chest X-ray/computed tomography \[CT\] and abdominal & pelvic CT/MRI with IV contrast, as well as a colonoscopy) * Previously documented history of familial adenomatous polyposis * Previously documented history of hereditary non-polyposis colorectal cancer diagnosed clinically (Amsterdam II criteria) or by genetic testing * History of inflammatory bowel disease * History of prior radiation treatments to pelvis * Clinically significant peripheral sensory or motor neuropathy (defined as symptomatic weakness, paresthesia or sensory alteration described to be interfering with function, interfering with activities of daily living, disabling or life-threatening) * History of any clinically significant cardiac disease (i.e., class 3-4 congestive heart failure, symptomatic coronary artery disease, uncontrolled arrhythmia, and/or myocardial infarction within the last 6 months) * History of uncontrolled seizures or clinically significant central nervous system disorders * History of psychiatric conditions or diminished mental capacity that could compromise the giving of informed consent, or interfere with study compliance * History of allergy and/or hypersensitivity to capecitabine and/or oxaliplatin * History of difficulty or inability to take or absorb oral medications * White blood cells (WBC) \>= 3000/mm\^3 * Absolute neutrophil count (ANC) \> 1,500/mm\^3 * Hemoglobin \> 9.5 mg/dl * Platelet count \>= 100,000/mm\^3 * Total bilirubin =\< 3 mg/dl * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.0 times institutional upper limit of normal (ULN) * Alkaline phosphatase =\< 2.0 times ULN * Creatinine clearance (CLcr) \>= 50 ml/min by Cockroft-Gault equation * Patients who have experienced a prior malignancy must have received potentially curative therapy for that malignancy, and must be cancer-free for at least five years from the date of initial diagnosis (exceptions: patients treated for non-melanoma skin carcinoma, or in-situ carcinomas) * Patients of reproductive potential must agree to use an effective method of birth control when undergoing treatments with known or possible mutagenic or teratogenic effects; all female participants of childbearing potential must have a negative urine or serum pregnancy test within two weeks prior to study registration