Issues of controllability and stabilization design for vehicle's lateral dynamics are presented. Based on the assumption of constant driving speed, a second-order nonlinear lateral dynamical model is obtained. It is observed that saddle node bifurcation will appear in vehicle dynamics with respect to the variation of the front wheel steering angle, which might result in spin and/or system instability. In order to possibly prevent the occurrence of such an instability, the controllability of vehicle dynamics at the saddle node bifurcation point is discussed. This leads to the design of a direct state feedback control law for system stabilization. Two-Parameter bifurcation analysis of system behavior is also obtained to classify the regime of the effective control gains for system stabilization. Numerical simulations for an example model demonstrate the effectiveness of analytical results.