Task and Motion Planning (TAMP) algorithms solve long-horizon manipulation tasks by integrating task planning with motion planning; the task planner proposes a sequence of actions towards a goal state and the motion planner verifies whether this action sequence is geometrically feasible for the robot. However, state-of-the-art TAMP algorithms do not scale well with the difficulty of the task and require an impractical amount of time to solve relatively small problems. We propose Constraints and Streams for Task and Motion Planning (COAST), a probabilistically-complete, sampling-based TAMP algorithm that combines stream-based motion planning with an efficient, constrained task planning strategy. We validate COAST on three challenging TAMP domains and demonstrate that our method outperforms baselines in terms of cumulative task planning time by an order of magnitude.