The saying "Just a Sinner saved by grace" is not confidence. We use this phrase to justify the complete lack of victory and forward momentum in our lives. Is that the gospel message? It's true that while we were yet sinners Christ died for us. But the moment you put your faith in Christ, sin lost its power!
Paul says: "Sin shall not have dominion over you." Why? Because you are not under law, but grace. You may still sin, but sinner is no longer your identity. Sinner is no longer your name.