This paper provides the foundation of connections between default reasoning and constraint satisfaction. Such connections are important because they combine fields with different strengths that complement each other: default reasoning is broadly seen as a promising method for reasoning from incomplete information, but is hard to implement. On the other hand, constraint satisfaction has evolved as a powerful, and efficiently implementable, problem solving paradigm in artificial intelligence. In this paper, we show how THEORIST knowledge bases and theories in Constrained Default Logic with prerequisite-free defaults may be mapped to partial constrained satisfaction problems. We also extend these results to deal with priorities among defaults.