Tositumomab and Iodine I 131 Tositumomab in Treating Patients With Chronic Lymphocytic Leukemia or Small Lymphocytic Lymphoma in First Remission

Inclusion Criteria: * Patients with a diagnosis of cluster of differentiation (CD)20+ CLL/SLL; prior to the first treatment patients with CLL must have been either Rai stage III/IV disease or Rai stage I/II with evidence of disease activity as defined by the National Cancer Institute (NCI) 1996 guidelines, and patients with SLL must have been Stage III or IV per Ann Arbor staging system * Patient has received prior therapy and is in 1st remission with a partial or complete response to treatment * Patients must have no more than 25% of the intratrabecular marrow space involved by leukemia in bone marrow biopsy specimens as assessed microscopically after completion of treatment; bilateral posterior iliac crest core biopsies are required if the percentage of intratrabecular space involved exceeds 10% on a unilateral biopsy; the mean of bilateral biopsies must be no more than 25% * Patient must have consented to participate in the study and signed and dated an appropriate institutional review board (IRB)-approved consent form that conforms to federal and institutional guidelines * Patient must have a Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1 or 2 (0 = fully active, able to carry on all pre-disease performance without restriction; 1 = restricted in physically strenuous activity but ambulatory and ambulatory and able to carry out work of a light or sedentary nature, e.g., light house work, office work; 2 = ambulatory and capable of all self-care but unable to carry out any work activities and is up and about more than 50% of waking hours) * Patient must have an anticipated survival of at least 3 months * Granulocytes \>= 1,500/uL within 14 days of planned dosimetric infusion * Platelets \>= 100,000/uL within 14 days of planned dosimetric infusion * White blood count =\< 20,000/mm\^3 * Serum creatinine \< 2 times upper limit of normal * Total bilirubin \< 2 times upper limit of normal * Aspartate aminotransferase (AST) \< 5 times upper limit of normal * Males and females must agree to use a contraceptive method from enrollment to 6 months after receiving I-131 labeled tositumomab Exclusion Criteria: * Patients who have received prior radiolabeled antibody * Patients with active hemolysis * Patients must not require sustained transfusion support of blood products * Patients in 2nd remission or beyond * Patients who have undergone treatment with either stem cell or bone marrow transplant * Patients with active obstructive hydronephrosis * Patients with evidence of any significant systemic illness, active hepatitis B infection or other active infection at the time of study entry * Patients with New York Heart Association class III or IV heart disease or other serious illness that would preclude evaluation * Patients with known human immunodeficiency virus (HIV) infection * Patients who are pregnant or nursing * Patients with prior malignancy other than CLL/SLL, except for adequately treated skin cancer (basal cell or squamous cell carcinoma), in situ cervical cancer, or other cancer for which the patient has been disease-free for 5 years unless approved by the principal investigator (PI) * Patients with active brain or leptomeningeal involvement by malignancy * Patients who have, in the opinion of the investigator, other medical, social, or psychosocial factors that may negatively impact compliance or their safety by participation in this study