This paper proposes a hybrid control approach to task priority based mobile manipulation. More specifically, it uses a hybrid systems framework to address the problem of end-effector path following for a manipulator attached to a nonholonomic mobile platform where the joints are subject to constraints and the inputs signals are required to be bounded. A switched control strategy allows the robot to avoid infeasible and singular joint configurations while executing a bounded pseudo-inverse based feedback control law. The resulting closed loop system stabilizes the desired path, has a dwell time in each mode, and only switches a finite number of times.