Therefore anyone who sets aside one of the least of these commands and teaches others accordingly will be called least in the kingdom of heaven, but whoever practices and teaches these commands will be called great in the kingdom of heaven. 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 5:19-20 NIV)
The passages of the New Testament that are known as the Sermon on the Mount are masterful teachings of the Master Teacher Jesus. He is crafting out a vision of the " kingdom come". The Masters vision is informative, challenging, and a bit overwhelming for us. Jesus sees the kingdom defined by a number of issues that were relevant to his first century audience (and still resonate today!)
Here he defines what righteousness is. Certainly Jesus knows that his substitutionary death on the cross is going to impute righteousness to millions who come to him in faith. The Apostle Paul would later write that he who "knew no sin, became sin" that we might become the righteousness of God. Righteousness ( ie., right standing before God) is given freely to us all as we trust Christ for our salvation. But that is not what Jesus is addressing here.
No, Jesus is not speaking of an unseen transfer that is transacted in the heavenly realms. He is speaking of that which can be witnessed by mere mortals. The Pharisees had become a group more known for there creative ways of circumventing the intentions of the Divine Law than for their Radical Obediences. They were better with excuses than execution, more adept at sidestepping than stepping up, they were half hearted followers ignoring the audience of One that they were to live for. Jesus addresses than head on.
What concerns Christ is not our claim to follow Him but our practics. Rather than being "righteous in name only" as the Pharisees were Jesus challenges his disciples to depth, to full obedience, to uncomfortable obediences, and to living out their faith out loud. It seems to me that Jesus was demanding righteousness than showed up in the real world. Are we the real deal? Is our obedience limited by convenience? By public approval? By comfort? It is time for real faith for the real world!