Under some emergencies, persons are required to arrive quickly at the scene and collaborate on sensitive tasks. To ensure effective performance of these tasks and be compliant with business regulations, user context should be considered and security requirements are desired. In this paper, we tackle this challenging problem of quick collaborative response from the view of task allocation with user authorization. The considered Quickresponse task allocation problem (QTAP) answers how to find a user-task allocation solution, the group of qualified users who can fastest arrive at the scene to fulfill the collaborative processes and satisfy the required security constraints. We study the computational complexity of this problem and solve it by the reduction to the well-studied scheduling problem. We further discuss an important extension of QTAP that supports task dependencies and propose an algorithm to solve it.