Answering questions with data is a difficult and time-consuming process. Visual dashboards and templates make it easy to get started, but asking more sophisticated questions often requires learning a tool designed for expert analysts. Natural language interaction allows users to ask questions directly in complex programs without having to learn how to use an interface. However, natural language is often ambiguous. In this work we propose a mixed-initiative approach to managing ambiguity in natural language interfaces for data visualization. We model ambiguity throughout the process of turning a natural language query into a visualization and use algorithmic disambiguation coupled with interactive ambiguity widgets. These widgets allow the user to resolve ambiguities by surfacing system decisions at the point where the ambiguity matters. Corrections are stored as constraints and influence subsequent queries. We have implemented these ideas in a system, DataTone. In a comparative study, we find that DataTone is easy to learn and lets users ask questions without worrying about syntax and proper question form.