Yes, the atonement and remission of sins is complete. Christ has bore God's Wrath (A Wrath that belongs to Father, Son, and Spirit) against sin, emptied death of its power and fear, and smashed the Devil's skull and his legion of demons with the Jaw-Bone of His own Humiliation. The Victory is for Christ and His Church. But the war is not over. As the Apostle tells us, we bear about the marks of Christ in our bodies. We are called into imitation, losing our lives so we may find them, bearing our own crosses towards Salvation's Hill.
We receive salvation, passively awoken by the grace of God (i.e. Jesus calling us). I think Augustine read the Scriptures rightly. But once we are awake, we are called into a life of battle, a repetition of Christ's victory over sin, death, and the devil. Some might call this the divide between justification and sanctification. I think that's poorly applying words to the reality. We are saved, we are being saved, and we will be saved.
But what many have lost is the demand for this kind of battle. It's not a battle waged by moralism or propping up cultural practices. It's not a battle waged through passivity and searching for nirvana. It's not a battle of medieval ladder climbing, turning sacraments into magik. It's the kind of battle many Christians have seen and engaged in many ways. To be a Christian is to be a disciple, and to be a disciple is to move, out of the love of God and our neighbor*, towards healing. It is to become a Human as a Human is supposed to be, namely Christ, which is why we are the diminutive (Christian means 'little Christ').
We war against the machinations of many sins. St. Paul lists many of them and calls them the 'fruit of the flesh'. Cut off from life, cut off from the Source of Life, we turn inward and feed off ourselves. What we find is greed, pettiness, lying, vicious jealousy, idolatry, sexual immorality, violence, murder, cruelty, contempt, etc. The work of the evil in us is not merely head-liners. Sin working in us produces sneering, gossip, two-facedness, saccharine niceness without compassion, manipulation, word-breaking, passive-aggression, and many more.
The war is doing battle with these. How? By using the Sword of the Spirit, the Word of God. What does this actually mean? I end with a quote from the Desert Fathers:
A brother asked one of the Fathers, What shall I do? My thoughts are always turned to lust without allowing me an hour’s respite, and my soul is tormented by it. He said to him, Every time the demons suggest these thoughts to you, do not argue with them. For the activity of demons always is to suggest, and suggestions are not sins, for they cannot compel; but it rests with you to welcome them, or not to welcome them. Do you know what the Midianites did? They adorned their daughters and presented them to the Israelites. They did not compel anyone, but those who consented, sinned with them, while the others were enraged and put them to death. It is the same with thoughts.
The brother answered the old man, What shall I do, then, for I am weak and passion overcomes me?? He said to him, Watch your thoughts, and every time they begin to say something to you, do not answer them but rise and pray; kneel down, saying, Son of God, have mercy on me.
Then the brother said to him, Look, Abba, I meditate, and there is no compunction in my heart because I do not understand the meaning of the words. The other said to him, Be content to meditate. Indeed, I have learned that Abba Poemen and many other Fathers uttered the following saying, The magician does not understand the meaning of the words which he pronounces, but the wild animal who hears it understands, submits, and bows to it. So it is with us also; even if we do not understand the meaning of the words we are saying, when the demons hear them, they take fright and go away.
*By neighbor, I mean and don't mean how most people understand this. One's neighbor is not just anyone, but could be anyone. The particularity is important. This is the difference between liberal thought and Christian thought. I will expand on this in another post.