Task and motion planning is one of the key problems in robotics today. It is often formulated as a discrete task allocation problem combined with continuous motion planning. Many existing approaches to TAMP involve explicit descriptions of task primitives that cause discrete changes in the kinematic relationship between the actor and the objects. In this work we propose an alternative, fully differentiable approach which supports a large number of TAMP problem instances. Rather than explicitly enumerating task primitives, actions are instead represented implicitly as part of the solution to a nonlinear optimization problem. We focus on decision making for robotic manipulators, specifically for pick and place tasks, and explore the efficacy of the model through a number of simulated experiments including multiple robots, objects and interactions with the environment. We also show several possible extensions.