This paper presents a novel adaptive cruise control (ACC) strategy that utilizes a command governor (CG) to enforce vehicle following constraints. The CG formulation relies on knowledge of the maximum possible braking deceleration of the lead vehicle and a tunable assumption regarding the lead vehicle velocity profile (offering different levels of conservatism) to modify wheel torque commands to ensure safe following. In particular, a safe following distance is defined as one in which the ego vehicle can avoid collision with the lead vehicle and maintain a sufficient following distance in the event that the lead vehicle exerts maximum braking deceleration. The CG seeks to adjust the wheel torque command such that the aforementioned constraint is satisfied at every step in a prediction horizon (i.e., at every step, if the lead vehicle exerts maximum braking deceleration, the ego vehicle can brake and remain outside of the aforementioned buffer zone), which requires an estimate of future lead vehicle behavior. In this work, we explore different levels of conservatism with regard to this assumption. Simulations are presented for a heavy-duty truck, using a stochastic lead vehicle model that has been calibrated with actual traffic data. Even for the most conservative lead vehicle prediction models, results show that this CG-based ACC strategy can reduce braking energy expended (used as a surrogate for fuel wasted) by up to 78%, while improving drivability and reducing total trip time.