We investigate the amount of radio spectrum required for reliable vehicle-to-vehicle (V2V) communication for traffic safety. The basic feature of the traffic safety application is that it uses periodical broadcasts of status messages containing the location and velocity of transmitting vehicles. In our study we consider two dominant technologies for V2V communication, namely IEEE 802.11p and self-organizing time division multiple access (STDMA). We analyze the spectrum demand for a dense highway scenario with a stringent reliability requirement. The results indicate that more than 80 MHz bandwidth is needed to achieve 99% reliability in certain cases. This is in stark contrast to current regulatory decisions that dedicate only 10 MHz bandwidth in 5.9 GHz band for safety purposes in intelligent transportation system (ITS) in Europe and US. Our results suggests that a substantial change would be required in either spectrum allocation or in V2V communication system design to achieve the required traffic safety.