The deaths of the Gracchi drove a permanent wedge between the Senate and the people causing two political factions to appear: Optimates, who were the champions of the patrician class and Populares, who were the champions of the plebs. These factions were more divided than the political parties in America today because in Rome it was a case of human survival -- wealth versus poverty rather than a battle over ideology.
The other fallout of the deaths of the Gracchi was the public perception of the destruction of the rule of law. For any political system to be legitimate, it must be willing to stand behind a legal system that will protect those without power. By stooping to assassination, the Senate had proved themselves illegitimate – no better than the barbarians they felt superior to.