Vehicular Ad hoc Networks (VANETs), while promising new approaches to improving road safety, must be protected from a variety of threats. Greedy behavior attacks at the level of the Medium Access (MAC) Layer can have devastating effects on the performance of a VANET. This kind of attack has been extensively studied in contention-based MAC protocols. Hence, in this work, we focus on studying the impact of such an attack on a contention-free MAC protocol called Distributed TDMA-based MAC Protocol DTMAC. We identify new vulnerabilities related to the MAC slot scheduling process that can affect the slot reservation process on the DTMAC protocol and we use simulations to evaluate their impact on network performance. Exploitation of these vulnerabilities would result in a severe waste of channel capacity where up to a third of the free slots could not be reserved in the presence of an attacker. Moreover, multiple attackers could cripple the channel and none could acquire a time slot.