Imprime PGG, Alemtuzumab, and Rituximab in Treating Patients With High Risk Chronic Lymphocytic Leukemia

Inclusion Criteria: * Diagnosis of CLL (Hallek, Cheson et al. 2008) manifested by: Minimum threshold peripheral lymphocyte count of 5 x 10\^9/L AND immunophenotypic demonstrations of a population of B lymphocytes (as defined by CD19+) which are monoclonal (light chain exclusion); CLL will be diagnosed if these cells have \>= 3 of the following characteristics: CD5+, CD23+, dim surface light chain expression, dim surface CD20 expression AND fluorescence in situ hybridization (FISH) analysis is negative for IGH/CCND1 and/or immunostaining is negative for cyclin D1 expression * \>= 1 of the following poor prognosis factors: unmutated IGHV (\< 2%) AND CD38 expression (\>= 30% cells positive on flow cytometry); unmutated IGHV (\< 2%) AND ZAP-70 expression (\>= 20% cells positive on flow cytometry); use of VH3-21 gene segment irrespective of mutation status AND CD38 expression (\>= 30% cells positive on flow cytometry); use of VH3-21 gene segment irrespective of mutation status AND ZAP-70 expression (\>= 20% cells positive on flow cytometry); 11q22-; 17p13- * Rai classification Stage 0, I or II that does not meet standard NCI-IWCLL criteria for treatment of CLL (Hallek, Cheson et al. 2008) * Limited CLL disease burden with no lymph nodes \> 5 cm in any diameter and splenomegaly \< 6 cm below left costal margin in midclavicular line at rest * Creatinine =\< 1.5 x upper normal limit (UNL) * Total bilirubin =\< 3.0 x UNL; if total is elevated, a direct bilirubin should be performed and should be =\< 1.5 x UNL * AST =\< 3.0 x UNL * Eastern Cooperative Oncology Group (ECOG) performance status (PS): 0, 1, or 2 * Negative serum pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only * Provide informed written consent * Willing to return to a Lymphoma Specialized Program of Research Excellence (SPORE) enrolling institution for follow-up * Willing to provide blood samples for correlative research purposes Exclusion Criteria: * Pregnant women * Nursing women * Men or women of childbearing potential who are unwilling to employ adequate contraception * New York Heart Association Class III or IV heart disease * Recent myocardial infarction (\< 1 month) * Uncontrolled infection * Infection with the human immunodeficiency virus/acquired immune deficiency syndrome (HIV/AIDS), serological evidence of active hepatitis B infection (HBsAg or HBeAg positive) or positive hepatitis C serology, as further severe immunosuppression with this regimen may occur * Evidence of active autoimmune hemolytic anemia, immune thrombocytopenia, or pure red blood cell aplasia * Other active primary malignancy requiring treatment or limits survival to =\< 2 years * Any major surgery =\< 4 weeks prior to registration * Any previous chemotherapy or monoclonal antibody treatment for CLL * Current use of corticosteroids; NOTE: previous corticosteroids are allowed