Despite the large body of work studying congestion control and adaptive routing in isolation, much less attention has been paid to whether these two resource-allocation mechanisms work well together to optimize user performance. Most analysis of congestion control assumes static routing, and most studies of adaptive routing assume that the offered traffic is fixed. In this paper, we analyze the interaction between congestion control and adaptive routing, and study the stability and optimality of the joint system. Previous work has shown that the system can be modelled as a joint optimization problem that naturally leads to a primal-dual algorithm with shortest-path routing using congestion prices as the link weights. In practice, the algorithm is commonly unstable. We consider three alternative timescale separations and examine the stability and optimality of each system. Our analytic characterizations and simulation experiments demonstrate how the step size of the congestioncontrol algorithm affects the stability of the system, and how the timescale of each control loop and homogeneity of link capacities affect system stability and optimality. The stringent conditions imposed for stability suggests that congestion price would be a poor feedback mechanism in practice.