In the Bible Matthew 5:48 it says: "Be ye therefore perfect, even as your Father which is in heaven is perfect." 
 
Heavenly Father expects us to be perfect. But achieving that is not just an earthly endeavor. Those efforts go on after we die. We are always striving to become better and better. 
 
You are absolutely right about Jesus' role in all of this. There is no way we can become perfect without Jesus atonement. He suffered for all our sins. Once we repent our sins are washed away through Jesus atonement and sufferings. Only through continued repentance can we eventually have the possibility of being perfect. 
 
 
We are expected to keep the commandments and do everything we can to become perfect.  
 
We can become perfect in certain things. We can be perfect for different commandments and principles. For example, people have lived and died and have not killed another human being. For that one particular thing - they may have lived a perfect life for that one principle. But we need to be perfect in all things - in all principles - in all commandments. But that is what eternity and Jesus is for. We have that opportunity if we keep all of God's commandments and through Jesus atonement and through repentance we can have the possibility of perfection.