It's striking that after the revolutionary beatitudes, Our Lord sums up with some reactionary-sounding language, almost as if he wants to be sure no one gets the wrong idea. He is not coming to abolish the law, but to fulfill it; indeed, Amen quippe dico vobis, donec transeat caelum et terra, jota unum aut unus apex non praeteribit a lege, donec omnia fiant.
A jot, or to use the Greek equivalent, an iota is the lowercase letter i. A tittle (in the Vulgate, apex) is the dot on top of the i, or an equivalent diacritical mark.
It's easy to see why, given the alphabetic metaphor, interpretations of the statement tend to revolve around the written law of the Old Testament. Catholic priests giving homilies will frequently assure their congregations that Jesus's words don't mean we need to (say) rid our fridges of bacon, perform the ritual purifications that Hassidic Jews still use before meals, observe Shabbat, etc., etc. What Jesus means is that the sensible parts of the law, the real parts of Old Testament law, like the ten commandments, are not going to pass away.
One can forgive both Jews and atheists for finding such convenient and seemingly ad hoc divisions between "real" and "unreal" parts of Old Testament practice unconvincing!
After all, while the ten commandments have a unique role in Judeo-Christian tradition, Jesus never actually refers to them--though he does refer to the two great commandments to love God and neighbor. Why not assume that those two are the "real" law, the law that doesn't pass away? Or, on the other hand, if the ten commandments are critical, why should we not assume that the penalties for violating them (such as the death penalty for blasphemy--a penalty which, unlike the one for adultery, Jesus's actions never seem to abrogate) are still parts of the real law, the law that matters from a Divine perspective?
One can of course sort these things out. But a sorting out of which parts of the Old Testament are key and which are not, from a Christian perspective, inevitably ends in appeals to what pre-modern and early-modern English thinkers called "the law of reason," or "the natural law."
And since that is the case, I wonder whether one might not cut to the chase and assume that Our Lord, when we speaks of the law which alters not one jot or tittle, is indeed speaking of the law of nature in its broad sense, the one that includes human nature and the moral codes that can be deduced from it.
This coheres of his otherwise arbitrary and seemingly hyperbolic statement that "until heaven and earth pass away" the smallest parts of the law will remain. Nature's law remains as long as nature remains; when earth passes away, and earthly natures are changed or ended, then indeed the natural law will pass away. The natural law will not pass away until, as is suggested in those even more puzzling words, omnia fiant, until "all be fulfilled," or, perhaps more literally, until "all is done." Until--to steal language from another part of the New Testament--it is finished.