Triapine and Gemcitabine Hydrochloride in Gallbladder Cancer

Inclusion Criteria: * Histologically or cytologically confirmed adenocarcinoma of the biliary ducts that is unresectable and/or metastatic; this can include unresectable or metastatic carcinomas of the Ampulla of Vater. In addition, unresectable or metastatic gall bladder carcinoma will be allowed * Measurable disease * No prior chemotherapy * Life expectancy of greater than 3 months * ECOG performance status =\< 2 (Karnofsky \>= 60%) * Leukocytes \>= 3,000/uL * Absolute neutrophil count \>= 1,500/uL * Platelets \>= 100,000/uL * Creatinine within normal institutional limits * Patients may have mildly abnormal liver function defined as a total bilirubin \> ULN and =\< 3x the institutional upper limits of normal (includes CTCAE v.3 grades 1-2 hyperbilirubinemia) * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients may not be receiving any other investigational agents * Patients with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events * History of allergic reactions attributed to compounds of similar chemical or biologic composition to Triapine or gemcitabine * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, or cardiac arrhythmia * Uncontrolled pulmonary disease including asthma, chronic bronchitis and COPD or with requirements for chronic oxygen use * Pregnant or lactating women * HIV infection * Patients with G6PD deficiency will be excluded in view of the potential for methemoglobinemia * Psychiatric illness/social situations that would limit compliance with study requirements