I started Louis Feldman's Jew and Gentile in the Ancient World. I have two items, which pertain to Jewish eschatology:
1. On page 26, Feldman states: "...we may note a Persian parallel to the motif that there will be six thousand years from the beginning of time to the final judgment of humanity by fire, and its Talmudic counterpart (Sanhedrin 97a-b), which quotes the Tanna de-vei Eliyahu as declaring that the world is to exist for six thousand years, the last two thousand of which will be the Messianic era; and this, according to tradition, will culminate in the Last Judgment."
I checked Babylonian Talmud Sanhedrin 97a-b, and there is actually a difference of opinion. One view is that the Messiah will come unexpectedly. Another idea is that he will come after the six thousand years of the world's existence, and that he could have come sooner, had it not been for "our many iniquities." According to this opinion, the Messianic era will last for two thousand years. Still another view is that those two thousand years will be a time of desolation, when the LORD alone will be exalted.
There are parallels between some of these ideas in the Talmud and the New Testament. Matthew 24:42 says that one should watch, because he does not know when his Lord will come. Revelation 20:4 talks about a Messianic era that will last for a thousand years. There is debate among Christians about whether or not we are in the millennium now. Some argue that we are currently in a Messianic age in which Christ rules and Satan is limited, meaning we're currently in the millennium (which is not a literal thousand years) that will precede the last judgment. Others contend, however, that Satan is still deceiving people, which is not supposed to be happening during the millennium (Revelation 20:3), showing that the millennium is still future.
I do think that there is a sense in which New Testament passages maintain that we are in a Messianic era, and that things that the prophets predicted about the Messianic era (or, if you will, prophecies that interpreters applied to that) were being fulfilled in Jesus Christ. W.D. Davies, in his essay about Paul in The Cambridge History of Judaism, Volume Three: The Early Roman Period, says that Paul was trying to fulfill the Hebrew Bible's prophecies about the Gentiles' worship of God under the Messiah. This makes sense, for Paul in Romans 15:12 quotes Isaiah 11:10, which concerns the reign of the root of Jesse, in whom the Gentiles will hope. Paul appeals to that verse to show his audience that God has welcomed the Gentiles. Was Paul saying that his time was the Messianic era in which the Gentiles would be included?
2. On page 98, Feldman talks about expectations among Jews and others that a Messiah would arise in the first century C.E. Josephus, in Jewish War 6.312-313, says that the Jews revolted against the Romans in 66 C.E. because an oracle in their Scriptures predicted that, at that time, someone from their country would assume rulership of the world. Tacitus, in Histories 5.13.2, says that Jewish ancient priestly writings said that, in the year 66, the East would increase in strength and men from Judea would take control of the world. Suetonius says the same sort of thing in Vespasian 4.5. These three people applied the prophecy to the emperor of Rome. Josephus, for example, notes that Vespasian assumed imperial authority while he was on Jewish land.
I talked about some of this in my post, Matthew 2:1-2: The Magi, in which I asked why the magi visited Jesus: "Why did the wise men (or magi) care about a newborn king in Judea, a subservient nation that lacked political power and prestige?" One solution I found was that the Magi believed that a ruler would come out of Judea, and so they wanted to honor him.
I also thought of Martin Luther's argument that Jesus was the Messiah because Daniel 9 says that the Messiah would come in the first century (according to him and many Christians), and Luther states that even first century Jews believed that. For Luther, either the Messiah came in the first century, or he is not coming, and so Jews are wrong to wait for a future Messiah; rather, Luther thinks they should embrace the Messiah who came, Jesus Christ. I wonder if Daniel 2 has something to do with Jews' dating the Messiah to the first century: if the fourth kingdom was understood as Rome, then the Messiah would overthrow Rome.