For I tell you that unless your righteousness surpasses that of the Pharisees and the teachers of the law, you will certainly not enter the kingdom of heaven.
Matthew 5:20
Again, as in verse 17, this all points to the cross. How can we have that perfect righteousness? There is no way we can earn it. We know that this is an impossible mountain we cannot climb.
It must be a gift. Someone must live perfectly and yet die on our behalf to save us from eternal death - the Lamb of God! (Isa 53!!)
What tension there must have been in the minds of the hearers here. Jesus is not revealing the ‘how’ just yet, but he sure is getting their attention. I think that many, trembling at his words, followed him with their weight of sin and guilt, knowing in their gut that this man had the answer, indeed, was the answer, and would somehow, oh, somehow, show them how to be rid of the crushing burden they were carrying.
Concerning the righteousness which is in the law, [I was] blameless. But what things were gain to me, I have counted loss for Christ. But indeed, I count all things loss...that I may gain Christ, and be found in Him, not having my own righteousness, which is from the law, but that which is through faith in Christ, the righteousness which is from God by faith.
Philippians 3:6-9
How wonderful this ‘surpassing’ righteousness is contrasted to Pharisaic righteousness.