Dasatinib in Treating Patients With Chronic Lymphocytic Leukemia

Inclusion Criteria:

* Written informed consent and Health Insurance Portability and Accountability Act (HIPAA) authorization for release of personal information
* Eastern Cooperative Oncology Group (ECOG) =\< 2
* In vitro dasatinib sensitivity (IC 50 =\< 50 nm per MTS assay)
* Diagnosis of CLL and must meet one of the following:

  * Relapsed CLL in all patients who have failed at least one prior treatment, regardless of risk group
  * OR De novo (treatment-naïve) patients age \>= 65 who are not candidates for or do not want to pursue aggressive chemotherapy treatment
* Have indications for treatment or evidence of progressive disease defined as follows (1996 NCI working group):

  * Massive or progressive splenomegaly
  * Massive lymph nodes (\>= 10 cm), nodal clusters (\>= 10 cm), or progressive lymphadenopathy
  * Symptomatic anemia and/or thrombocytopenia (Rai stages III or IV disease)
  * Autoimmune hemolytic anemia and/or thrombocytopenia that are poorly responsive to corticosteroid therapy
  * Progressive lymphocytosis with increase in lymphocyte count of \>= 50% over a 2-month period or an anticipated doubling time of \< 6 months
  * Repeated episodes of infection
* Have not received CLL treatment within the past 2 weeks
* Total bilirubin \< 2.0 x upper limit of normal (ULN)
* Aspartate aminotransferase (AST) =\< 2.5 x ULN
* Alanine aminotransferase (ALT) =\< 2.5 x ULN
* Serum creatinine \< 2.0 x ULN
* International normalized ratio (INR) =\< 1.2
* Platelet (Plt) count \> 30,000
* Ability to take oral medication (dasatinib must be swallowed whole)
* No clinically significant infections as determined by the investigator
* Normal corrected QT (QTc) interval (\< 450 msec)
* Serum potassium and magnesium are within normal limits
* Women of childbearing potential (WOCBP) must have a negative serum or urine pregnancy test (sensitivity =\< 25 IU HCG/L) within 72 hours prior to the start of study drug administration
* Persons of reproductive potential must agree to use an adequate method of contraception throughout treatment and for at least 4 weeks after study drug is stopped prior to study enrollment; women of childbearing potential must be advised of the importance of avoiding pregnancy during trial participation and the potential risk factors for an unintentional pregnancy
* After consent, discontinuation ("washout period") of any medications known to contribute significantly to the risk of QT prolongation or interfere with cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4) mediated drug metabolism
* Patient agrees to discontinue St. John's Wort while receiving dasatinib therapy (discontinue St. John's Wort at least 5 days before starting dasatinib)
* Patient agrees that IV bisphosphonates will be withheld for the first eight weeks of dasatinib therapy due to risk of hypocalcemia
* Patient agrees to discontinue anti-coagulants and anti-platelet drugs; note: a low dose aspirin regimen (81mg QD) is permitted with close monitoring of the subject's platelets for a level \>= 50,000/mm\^3

Exclusion Criteria:

* Patients may not receive concurrent chemotherapy, radiotherapy, or immunotherapy
* Pleural or pericardial effusion of any grade
* Uncontrolled angina, \> New York Heart Association (NYHA) class III congestive heart failure or myocardial infarction (MI) within 6 months prior to study enrollment
* Diagnosed congenital long QT syndrome
* Any history of clinically significant ventricular arrhythmias (such as ventricular tachycardia, ventricular fibrillation, or Torsades de pointes)
* Prolonged QTc interval on pre-entry electrocardiogram (\> 450 msec)
* Subjects who are detained or imprisoned are not eligible
* History of significant bleeding disorder unrelated to cancer, including:

  * Diagnosed congenital bleeding disorders (e.g., von Willebrand's disease)
  * Diagnosed acquired bleeding disorder within one year (e.g., acquired anti-factor VIII antibodies)
* May not take concomitant medications that are generally accepted to have a risk of causing Torsades de Pointes including: (patients must discontinue drug 7 days prior to starting dasatinib)

  * Quinidine, procainamide, disopyramide
  * Amiodarone, sotalol, ibutilide, dofetilide
  * Erythromycin, clarithromycin
  * Chlorpromazine, haloperidol, mesoridazine, thioridazine, pimozide
  * Cisapride, bepridil, droperidol, methadone, arsenic, chloroquine, domperidone, halofantrine, levomethadyl, sparfloxacin, lidoflazine
* Patients already taking other CYP inducers or inhibitors other than those listed above are eligible for the study only after principal investigator (PI) review; dose adjustments and/or monitoring of drug levels where applicable will be made as needed by the PI after consultation with pharmacy
* Women who:

  * Are unwilling or unable to use an acceptable method to avoid pregnancy for the entire study period and for at least 4 weeks after cessation of study drug, or
  * Have a positive pregnancy test at baseline, or
  * Are pregnant or breastfeeding