The United States is deploying the broadband wireless network for public safety and emergency response. While this will provide a foundational network when disasters or other emergencies appear, the network capacity could still be insufficient when large scale emergency events, such as earthquakes or flooding, happen. On-demand broadcast is a possible solution to address this situation, but its effectiveness remains unknown. In this paper, we aim to uncover the effectiveness of on-demand broadcast at different situations. Specifically, we study the scaling of average response time on the information requests with regard to the indicators of the content diversity - the number of distinct content files and the content popularity distribution. To achieve this goal, we first derive the lower bound of the average response time. We further investigate broadcast for streaming videos and uncover that parallel broadcast could have the same lower bound as the sequential broadcast under certain conditions. Based on the lower bound we derived, we evaluate the scaling of response time with regard to the number of files under different distributions. We further provide numerical results to demonstrate the accuracy of the approximation and the value of the lower bound on evaluating the optimality of a basic heuristic on-demand broadcast scheme.