Clogging Denial of Service (DoS) attacks have disrupted or disabled various networks, in spite of security mechanisms. External adversaries can severely harm networks, especially when high-overhead security mechanisms are deployed in resource-constrained systems. This can be especially true in the emerging standardized secure Vehicular Communication (VC) systems: mandatory message signature verification can be exploited to exhaust resources and prevent validating incoming messages sent by neighboring vehicles, information that is critical, often, for transportation safety. Efficient message verification schemes and better provisioned devices could serve as potential remedies, but existing solutions have limitations. We point out those and identify, challenges to address for scalable and resilient secure Vehicular Communication (VC) systems, and, most notably, the need for integrating defense mechanisms against clogging Denial of Service (DoS) attacks. We take the position that existing secure Vehicular Communication (VC) protocols are vulnerable to clogging Denial of Service (DoS) attacks and recommend symmetric key chain based pre-validation with mandatory signature verification to thwart clogging Denial of Service (DoS) attacks, while maintaining all key security properties, including non-repudiation to enable accountability.