Climate change is expected to have impacts on our surface water resources, especially on the deterioration of surface water quality. The objectives of this study were to develop a calibrated and validated watershed model for daily streamflow and daily fecal coliform bacteria (FCB) concentrations using the Soil and Water Assessment Tool (SWAT) for the Big Sunflower River Watershed (BSRW) and to assess the sensitivity of FCB concentrations to changes in precipitation, temperature, and CO2 concentrations. The model demonstrated reasonable performances in simulating daily stream flow (R2 = 0.64–0.77, NSE = 0.57–0.75) and FCB concentrations (R2 = 0.56–0.60, NSE = 0.23–0.40) as compared to the previous literature. The one-at-a-time sensitivity analyses showed that average FCB concentrations were sensitive to changes in rainfall, temperature, and CO2 concentrations. Increased rainfall caused greater wash-off of FCB colonies from soil surfaces, while increased temperatures caused a decrease in surface water bacteria concentrations due to increased bacteria die-off rates. The CO2 concentration parameter was determined as the least sensitive parameter in this study.