The context here is the Law of Moses, not the end of the world.
The negative argument
I do not believe the passage is telling us anything about the timing or circumstances of the end of the world.
The phrase "until heaven and earth pass away" is the language of covenant or contract. Most contracts include a "Force Majeure" clause indicating that, if certain extreme events occur, you are excused from the obligations of the contract (see here).
For example, most insurance policies don't cover damage caused by war; most commercial contracts provide excusal in case of natural disasters.
The Greek word here rendered "until" is ἕως, which carries meanings including: "until, as far as, up to, as much as" (see here).
Jesus is indicating that there is no "Force Majeure" clause to His words. No matter what--as much as the heavens and the earth being destroyed could happen--yet He will make good on His words.
That Jesus saw His words in this sense is found in Matthew 24:35:
Heaven and earth shall pass away, but my words shall not pass away.
That's a pretty solid "no matter what"; you won't find any legal document giving that strong a guarantee.
Similar concepts are expressed in Isaiah 49:14-16 & Joshua 21:45
The positive argument
The question is not when will the heavens and the earth pass away--this is nowhere to be found in the context of this passage--the question is about the Law of Moses. People are concerned that Jesus is destroying the Law and Jesus is responding.
Note that the Law of Moses is frequently referred to at the time as "The Law"--e.g. see Hebrews 7:11, Hebrews 9:19, Galatians 2:15-16. This is not a discussion of all laws, this is a discussion of the Law given to Moses.
When was the Law of Moses fulfilled?
The Law of Moses was fulfilled by Jesus' sacrifice, not in AD 70 or at the end of the world.
There may be an allusion to this in the passion account of John:
When Jesus therefore had received the vinegar, he said, It is
finished: and he bowed his head, and gave up the ghost. (John 19:30)
But either way the allusion is unmistakable in the passion account of Matthew:
And, behold, the veil of the temple was rent in twain from the top to
the bottom (Matthew 27:51)
The significance of the rending of the veil is brought home in Hebrews 9:
And after the second veil, the tabernacle which is called the Holiest
of all; (verse 3)
But into the second went the high priest alone once every year, not
without blood, which he offered for himself, and for the errors of the
people: (verse 7)
But Christ being come an high priest of good things to come, by a
greater and more perfect tabernacle, not made with hands, that is to
say, not of this building; (verse 11)
Neither by the blood of goats and calves, but by his own blood he
entered in once into the holy place, having obtained eternal
redemption for us. (verse 12)
Jesus parted the veil and redeemed the human family, an act for which the prior actions of the high priest were a symbol.
The testament put into effect by Jesus' sacrifice
That this is a reference to Jesus' death is made explicit a few verses later:
15 And for this cause he is the mediator of the new testament, that
by means of death, for the redemption of the transgressions that
were under the first testament, they which are called might receive
the promise of eternal inheritance.
16 For where a testament is, there must also of necessity be the
death of the testator.
17 For a testament is of force after men are dead: otherwise it is
of no strength at all while the testator liveth.
It certainly took the people at the time a while to understand that the ordinances of the Law of Moses were fulfilled (hence documents like Galatians, Romans, Hebrews), but the Law of Moses was fulfilled by Jesus' death.
Important clarification--I'm not arguing that everything was fulfilled/complete/finished at the time of Jesus' atoning sacrifice, but that specifically the Law of Moses was fulfilled. That context is critical--He is responding to concerns about the Law of Moses.
Jesus did not destroy or violate the Law, He complied with and completed the Law and fulfilled the covenant made with Israel--bringing a new covenant in its place.