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Planning and execution of agile locomotion maneuvers have been a longstanding challenge in legged robotics. It requires to derive motion plans and local feedback policies in real-time to handle the nonholonomy of the kinetic momenta. To achieve so, we propose a hybrid predictive controller that considers the robot's actuation limits and full-body dynamics. It combines the feedback policies with tactile information to locally predict future actions. It converges within a few milliseconds thanks to a feasibility-driven approach. Our predictive controller enables ANYmal robots to generate agile maneuvers in realistic scenarios. A crucial element is to track the local feedback policies as, in contrast to whole-body control, they achieve the desired angular momentum. To the best of our knowledge, our predictive controller is the first to handle actuation limits, generate agile locomotion maneuvers, and execute optimal feedback policies for low level torque control without the use of a separate whole-body controller.