Tasks in mobile manipulation planning often require thousands of individual motions to complete. Such tasks require reasoning about complex goals as well as the feasibility of movements in configuration space. In discrete representations, planning complexity is exponential in the length of the plan. In mobile manipulation, parameters for an action often draw from a continuous space, so we must also cope with an infinite branching factor. Task and motion planning (TAMP) methods integrate logical search over high-level actions with geometric reasoning to address this challenge. We present an algorithm that searches the space of possible task and motion plans and uses statistical machine learning to guide the search process. Our contributions are as follows: 1) we present a complete algorithm for TAMP; 2) we present a randomized local search algorithm for plan refinement that is easily formulated as a Markov decision process (MDP); 3) we apply reinforcement learning (RL) to learn a policy for this MDP; 4) we learn from expert demonstrations to efficiently search the space of high-level task plans, given options that address different (potential) infeasibilities; and 5) we run experiments to evaluate our system in a variety of simulated domains. We show significant improvements in performance over prior work.