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This paper deals with day-ahead static security assessment with respect to a postulated set of contingencies while taking into account uncertainties about the next day system conditions. We propose a heuristic approach to compute the worst-case under operation uncertainty for a contingency with respect to overloads. We formulate this problem as a non-convex nonlinear bilevel program that we solve approximately by a heuristic approach which relies on the solution of successive optimal power flow (OPF) and security-constrained optimal power flow (SCOPF) problems of a special type. The method aims at revealing those combinations of uncertainties and contingencies for which the best combination of preventive and corrective actions would not suffice to ensure security. Extensive numerical results on a small, a medium, and a very large system prove the interest of the approach.