Like I said one needs to distinguish when asking this question. There are two Christs.
1. Christ the son of God as per Christian doctrine
2. Christ the yet another Jewish prophet as per likely historical fact
For case
no. 1 the answer is yes. This can be seen in Pilate’s judgement scene in Luke, John and Mark where the Jews are presented as crying “Crucify him†(Christ). The reason for Christians blaming Jews for their spiritual leader’s death is obvious. Until the second century Christianity was part of Judaism and all Christians were Jews, most in fact born so since Greek and other converts were few. By the fourth when the four Gospels were unofficially canonised they are a separate religion that no longer seeks to convert Jews but only Romans. It derives legitimacy by claiming to be the “true†inheritor of Jewish scriptural tradition and struggles to detach its followers from Judaism, both of which lead to its attempts at discrediting it (e.g. the Adversus Judaeus homilies by most Church fathers). This is also the cause of anti-Semitism as a special form of religious intolerance unique to Abrahamic religions. If the relationship between the two had turned out different (say Christianity dominated Judaism and stopped trying to convert Romans) then Christian doctrine would have blamed Jesus’ death on Romans.
Britannica > Origin of Christianity: the early Christians and the Jewish community
Largely owing to the discoveries at Qumran, many scholars now regard primitive Christianity, with its apocalyptic and eschatological interests, as part of a broad spectrum of attitudes within Judaism itself, rather than as peripheral to Jewish development or to the norm set by Pharisaic Judaism. Indeed, Jesus himself may now be classified as an apocalyptic prophet whose announced intentions were not to abrogate the Torah but to fulfil it.
For case
no. 2 the answer is no. The Romans ruled Palestine at the time and had the historical Jesus executed. He was just another subversive and prophet claiming to be the Messiah, of the sort with which Palestine was rife at the time. The Jews had been conquered by the Romans and were expecting their Messiah to come soon, to set them free and restore their kingdom. Not surprisingly more than a few fanatics were willing to put themselves forward for the job. Today their equivalents are prophesying the End of Days in street corners, wearing cardboard signs or declaring Jihad in Iraq. The comparison is not entirely fair of course because at the time everyone believed the Messiah would come soon and indeed early Christians expected to see the Second Coming in their lifetimes for several centuries. The leaders of the Second and Third Jewish revolts were billed as the Messiahs and this is the main reason leading to schism between Christians and other Jews since the first already had their Messiah.
War Angel is right. Jesus was just one of the hundreds of thousands - 1 million Jews murdered by Rome during its occupation of Israel before the scattering.
Rome killed hundreds of thousands, if not over a million Jews, Jesus was one of them, his name just stuck.
The figure of 1.1 million, I am guessing you are citing in Josephus’ account, is absurd. The Empire’s population at the time was about 60 million and the World’s about 300. All historians of the times engaged in inflating numbers, for a variety of reasons and since many of them were Greek I hazard that boosting sales figures was one of them. Herodotus assigns 1.7 million men to Xerxes’ army and Thucydides similarly inflates the number of victims of the Peloponnesian War. Cassius Dio claims 240,000 Greek Romans massacred by Jews in Cyprus and another quarter of a million in Cyrene during the 115 CE Jewish revolts. He also cites half a million for Jewish dead during the Second Jewish revolt, while the Torah puts the number of dead to more than the number of the total inhabitants of the are at the time.
The accessibility of statistics, independent estimation, map information, calendar consistency and dispassionate objectivity we expect today were largely absent at the time and help explain these inflated numbers. This is not to invalidate their work but to see it in its proper context; they are still the best sources we have and neither is modern historiography free of such issues.
Before the 66 CE revolt, attributed to friction between the Jewish majority and the Greek communities, Roman rule in Palestine was benign by the standards of the time or indeed the Empire, for example Jews were exempt from military service and allowed to keep their customs.
Britannica > Roman occupation and Jewish revolts When the Romans had entered Palestine in 63 BC, they practiced a relatively humane occupation until c. AD 66–70. They did not interfere with religious practices unless they considered them a threat to Rome, and their rights of requisition were precise and limited.
Britannica > Relations between Jewish areas and nearby Gentile areas
In the 1st century, Rome showed no interest in making the Jews in Palestine and other parts of the empire conform to common Greco-Roman culture. A series of decrees by Julius Caesar, Augustus, the Roman Senate, and various city councils permitted Jews to keep their own customs, even when they were antithetical to Greco-Roman culture. For example, in respect for Jewish observance of the Sabbath, Rome exempted Jews from conscription in Rome's armies. Neither did Rome colonize Jewish Palestine. Augustus established colonies elsewhere (in southern France, Spain, North Africa, and Asia Minor), but prior to the First Jewish Revolt (AD 66–74) Rome established no colonies in Jewish Palestine.