There is a significant interest in utilizing demand response (DR) programs to increase the flexibility of sustainable power systems. The DR operators (e.g., aggregator companies) need a robust means to assess the performance of a potential DR program that will be employed in the future. Such assessments should be based on data, some of which are hardly available. Knowledge about the DR providers (e.g., the behavior of proactive consumers) is key to the success of a DR program. In this paper, we devise a data-driven framework to assess the impact of uncertainties associated with future DR programs. The proposed framework comprises two modules: the DR simulation module, and the data analytics module. The DR module solves an optimization problem which simulates the operation of a hypothetical DR program. The data analytics module, firstly, selects subsets from historical load and price data. Secondly, it performs sensitivity analysis on the optimal solution to capture the impact of uncertainties. We consider two sources of uncertainty. First, we consider lack of information about DR providers due to the absence of a DR program in the current system. Second, we consider errors in load and price forecasts, whose impacts are investigated by formulating a sensitivity matrix from the perturbed KKT equations of the optimization problem solved by the DR module. The proposed framework provides insights regarding the potential of a prospective DR program. Such information can be useful for DR operators as a starting point to decide their position in the contractual agreement they will engage in with the (distribution) system operator and/or DR providers in the future.