The cancer stem cell hypothesis suggests that tumors contain a small population of cancer cells that have the ability to undergo symmetric self-renewing cell division. In tumors that follow this model, cancer stem cells produce various kinds of specified precursors that divide a limited number of times before terminally differentiating or undergoing apoptosis. As cells within the tumor mature, they become progressively more restricted in the cell types to which they can give rise. However, in some tumor types, the presence of certain extra- or intracellular signals can induce committed cancer progenitors to revert to a multipotential cancer stem cell state. In this paper, we design a novel mathematical model to investigate the dynamics of tumor progression in such situations, and study the implications of a reversible cancer stem cell phenotype for therapeutic interventions. We find that higher levels of dedifferentiation substantially reduce the effectiveness of therapy directed at cancer stem cells by leading to higher rates of resistance. We conclude that plasticity of the cancer stem cell phenotype is an important determinant of the prognosis of tumors. This model represents the first mathematical investigation of this tumor trait and contributes to a quantitative understanding of cancer.