Maybe Paul proposes a greater distinction between Law and Gospel than Jesus does. Matthew 5:17"Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them. 18I tell you the truth, until heaven and earth disappear, not the smallest letter, not the least stroke of a pen, will by any means disappear from the Law until everything is accomplished. 19Anyone who breaks one of the least of these commandments and teaches others to do the same 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. 20For 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."
And in other passages, Jesus sums up the Law as loving God entirely, and loving others as we love ourselves; following the Golden Rule, taking up his cross and following him. So, he's certainly not telling us to forget about God's commandments and just to believe in him. He's requiring action from us as well.
So why do we distinguish between Law and Gospel? What God has joined together, let not man separate.

Distinguishing between law and gospel does not mean pitting one against the other, as if we want to keep one and eliminate the other. In fact, we don't even want more of one and less of the other. Distinguishing between law and gospel means making sure that they are both used for their proper purpose - and not reversed. Jesus' sermons did often emphasize the law - he was in some ways redefining it for the Jewish teachers who had corrupted it. But Jesus did not offer salvation through the law. When he was asked 'what must I do to be saved' and he answered, "Be perfect..." Jesus was not offering hope through the law. He was destroying hope in that path. Paul does the same. He reminds us that the law is not our enemy - but it is not our Savior either.