Fludarabine, Rituximab, and Alemtuzumab in Treating Patients With Chronic Lymphocytic Leukemia

Inclusion Criteria:

* Specific Diagnosis of B-Cell CLL
* An absolute lymphocytosis of \> 5,000/μL
* Morphologically, the lymphocytes must appear mature with \< 55% prolymphocytes
* Bone marrow examination must include at least a unilateral aspirate and biopsy; the aspirate smear must show \> 30% of all nucleated cells to be lymphoid or the bone marrow core biopsy must show lymphoid infiltrates compatible with marrow involvement by CLL; the overall cellularity must be normocellular or hypercellular
* Local institution lymphocyte phenotype must reveal a predominant B-cell monoclonal population sharing a B-cell marker (CD19, CD20, CD23) with the CD5 antigen, in the absence of other pan-T-cell markers; additionally, the B-cells must be monoclonal with regard to expression of either κ or λ and have surface immunoglobulin expression of low density; patients with bright surface immunoglobulin levels must have CD23 co-expression
* Patients must be in the intermediate- or high-risk categories of the modified three-stage Rai staging system (i.e., stages I, II, III, or IV)
* Patients in the intermediate-risk group must have evidence of active disease as demonstrated by at least one of the following criteria:

  * Massive or progressive splenomegaly, hepatomegaly and/or lymphadenopathy;
  * Presence of weight loss \> 10% over the preceding 6 month period;
  * Grade 2 or 3 fatigue;
  * Fevers \> 100.5°F or night sweats for greater than 2 weeks without evidence of infection;
  * Progressive lymphocytosis with an increase of \> 50% over a 2 month period or an anticipated doubling time of less than 6 months
* No prior therapy for CLL including corticosteroids for autoimmune complications that have developed since the initial diagnosis of CLL
* No medical condition requiring chronic use of oral corticosteroids
* Performance Status 0 - 2
* Due to alterations in host immunity, patients with HIV may not be enrolled
* Due to the unknown teratogenic potential of alemtuzumab, pregnant or nursing women may not be enrolled; women and men of reproductive potential should agree to use an effective means of birth control
* Creatinine =\< 1.5 x upper limit of institutional normal value
* Coomb's Testing NEGATIVE