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

* 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