The Judaism of Jesus' day had three main components whose roots you can see in the Old Testament.
One component was the temple and the worship associated with it. Its Scriptural roots are in the Levitical laws of Moses, after the exile it is expressed in the temple/priest-and-Levite focus in Chronicles, Ezra, and Nehemiah, and in Jesus' day it was championed by the Sadducees (i.e., the high priestly family and its partisans).
The second component was the law. Its roots are in the bulk of Moses' legal corpus, after the exile it appears in the person of Ezra the scribe and in his and Nehemiah's reforms pertaining to intermarriage, the Sabbath, and so forth, and in Jesus' day it was championed by the Pharisees in local synagogues.
The third component was the coming reign of God. Its roots are in "day of Yahweh" prophecies throughout the prophets, during and after the exile it takes on an increasingly apocalyptic tone and style in Daniel and in parts of Ezekiel and Zechariah, and in Jesus' day it was championed most forcefully by insurrectionist Zealots and by the kind of community that lived at Qumran and wrote/transcribed the Dead Sea Scrolls.
These three components are not discrete categories. Most likely the mass of Jews were influenced by and held to all three of them. Even the leaders of these components held to all three for the most part despite their emphasis on one in particular.
Jesus, in his person, life, and teaching, adopts all three and transforms all three.
Jesus maintains that temple-worship is crucial, but he maintains that his body itself is the temple. Paul describes the church as Jesus' body and thus the temple of God so that anyone who is part of it can worship, as Jesus said, "in spirit and in truth." The author of Hebrews points out that Jesus' sacrificial death gave access to the true temple in heaven to those who believe in him.
Jesus insists that the law will never go away but also that he is the living fulfillment of it, the one Paul calls "the goal [telos] of the law" (Rom. 10:4), the one the author of Hebrews says establishes a new covenant. What distinguishes the new covenant and its law from the old one is not its content but its location—it applies inside a person's heart and mind, not outside on a person's body—and its permanence—Christ's sacrifice and the forgiveness that comes from it is once-and-for-all. Anyone associated with Christ is by nature a lawkeeper because that person keeps the Living Law himself who transforms his or her nature into Jesus' own by his Spirit.
Jesus relentlessly asserts that the reign of God is close, but he insists the the reign of God is an invisible reality that exists wherever there is someone who submits to it and to Jesus, its king, even now despite the powers-that-be. It's a reign that's not of this world but works invisibly through all of it like yeast through dough. The reign of God will become visible when Jesus returns in glory but will be inherited only by those who receive it now while it's hidden by receiving Jesus himself.
In sum, Jesus takes the physical temple, law, and coming reign of Judaism and converts them into a spiritual temple, law, and coming reign all located in himself but which have physical results in the behavior of those who believe in him.
In the Jewish revolt against Rome in A.D. 66-73, the physical temple was destroyed. In that war, the Kitos War of 115-117, and the Bar Kochba Revolt of 132-136, attempts to establish a physical reign by force were crushed. The only options that remained to Judaism in the second century were the physical law on the one hand and the spiritualized versions of temple, law, and reign in Christianity on the other. From that time on, almost all Jews chose the former.
It is interesting that with the founding of the state of Israel the physical reign of Judaism has at least partially been reestablished after a long hiatus (partially in that it is not a legal theocracy). It is also interesting how many Christians are eager for Israel's physical law, physical reign, and (as they hope) physical temple to reappear and coalesce given that the church has confessed for 2,000 years that we already possess the true and eternal forms of all three in Christ. (That's probably a post for another time.)