Jesus lived at a time of complex political and religious struggles in Jerusalem. Jerusalem wasn't some out of the way holy site - during Jesus' time it was major city, filled with conflicting sects, all under Roman rule. Law and order was tenuous at the best of times, and the Romans would show no mercy putting down unrest, nor would they hesitate to come down hard on supposed troublemakers.

The vast majority of Jerusalem's population was Jewish at the time of Jesus' death, but the city itself was ruled by the Romans. The Romans gave the Jews wide latitude in religious affairs, and would have taken someone like Jesus disturbing the religious powers-that-be quite seriously. Saying that these high priests (the Sanhedrin) were 'the Jews' is like saying the pope is 'the Christian' - it glosses over vast and sometimes bloody differences. Jesus' first followers were Jews, most of those that helped him were Jews - and he was, of course, Jewish himself. That being said, other Jews could have very obviously been against him, seeing as he spoke out against a wide variety of religious rites that they held quite dear.

That being said, the Romans are widely held to be the ones that put Jesus to death. Whether they did so at the instigation of local leaders, in the interest of keeping order, is another thing altogether. But there was a complex factionalism at work, and the idea that some uniform and villainous (not to mention anti-Semitic) 'the Jews' were responsible is historically ridiculous.

This is somewhat tangential (so mods feel free to delete as you see fit) but the Catholic Church addressed this in 1965 in the Second Vatican Council. Specifically, the Declaration on the Relation of the Church with Non-Christian Religions Nostra Aetate says

True, the Jewish authorities and those who followed their lead pressed for the death of Christ; still, what happened in His passion cannot be charged against all the Jews, without distinction, then alive, nor against the Jews of today.

So the Catholic Church, at least, says that the Jews in general are not responsible for the death of Christ.