Jeremiah 31 verses 30-33 (or 31-34, depending on the edition) is often cited by Christians who identify the new covenant mentioned there with Jesus or with the New Testament. Skeptics argue that because Christians do not abide by the whole Torah, this verse cannot apply to the covenant that Jesus established.

The first thing to realize is that Torah is not equated with 'law'. Torah is instruction, teaching, the revelation of God's will and intent. It comes in many forms: laws, narrative, proverbs, oracles.

From the Rabbinic scholar Solomon Schecter:
> It must first be stated that the term Law or Nomos is not a correct rendering of the Hebrew word Torah. The legalistic element, which might rightly be called the Law, represents only one side of the Torah. To the Jew the word Torah means a teaching or an instruction of any kind. It may be either a general principle or a specific injunction, whether it be found in the Pentateuch or in other parts of the Scriptures, or even outside of the canon. The juxtaposition in which Torah and Mizwoth, Teaching and Commandments, are to be found in the Rabbinic literature, implies already that the former means something more than merely the Law...

As for the objection that 'no one will teach anyone else about God, because all will know God,' and since Jesus didn't bring this about, he cannot be this new covenant:

The phrase 'every man' is regularly used in the OT contextually to refer to something non-universal:
> Exod. 1:1 Now these are the names of the children of Israel, which came into Egypt; every man and his household came with Jacob.
> Ex. 7:12 For they cast down every man his rod, and they became serpents: but Aaron's rod swallowed up their rods.

Every man in the world had a rod? No, this is obviously limited, and while 'every man' is used in some places in a universal sense (as in the Flood judging all), the content is determined by context, and in Jeremiah 31:34 that context is 'the house of Israel' (Jer. 31:33) -- who is now all who believe and accept the Messiah.