There are a number of scriptures that talk about the strengthening power of the Atonement. My two favorites are found in Ether 12:27 and D&C 84:33. The first says that the Lord's grace (read: Atonement) is powerful unto "making the weak things strong unto them." The second says that he that is faithful unto the obtaining of the two Priesthoods is sanctified by the Spirit "even unto the renewing of their bodies." I'm sure that there are a number of scriptures that you can think of that refer to a time when the Lord strengthened His children as opposed to just fixing the problem.
From this perspective, it is easy to understand that we ought to seek the Lord for help in fortifying ourselves such that what normally would have caused a problem in our lives, be it temptation or affliction, is no longer a disturbance to our everyday happiness and eternal progression because we are now "stronger than that."
To take a mundane example, I'll speak of my love of onions and my love for my wife. I love onions on a lot of things including, but definitely not limited to, hamburgers, pizza, salad, and soup. However, my wife hates the smell of onions on my breath. Now, I can either have this be a constant temptation and sacrifice, or I can allow the love of my wife to overpower my love for onions. This is just what I have done. I tell you, when we go out to eat, there is neither sacrifice nor temptation in my heart when I ask that they hold the onions because making my wife happy is a far higher priority than making my tongue happy. The loving relationship overcomes a temporal love.
A brother at my ward mentioned that he felt that the Atonement was not just the power to evolve the behavior (giving us strength to resist the temptation), but that it was also the power to keep the person from being tempted at all by x-y-z temptation. I found this very intriguing because, as Elder Oaks said in his October 2006 General Conference address, the Atonement has the power to heal everything. I have no reason to believe that this does not include our temptations.
This fits with my concept of God and the relationship that He wants to have with us. The scriptures are clear that the Lord wants to have a relationship with us as close as a husband and wife have (the bride and bridegroom parables, for example). I commented to my wife the other day that she and I have no rules in between us. Why is that? Of course, it's because we know each other so well that we almost automatically know what will make each other happy or sad. Moreover, we respect each other so much that we have no desire to do those things that make each other sad. They are not even temptations. This state of relationship is obviously because we have opened ourselves up enough to become emotionally tied together in such a way that does not exist with us and any other mortal in the world.
If the Atonement is the "At-ONE-Ment" and the purpose of our life is to develop a relationship with God, doesn't it make sense that the Atonement is supposed to help us develop this relationship and that this relationship will enable us to know what we should and shouldn't do and have no desire to do the things we shouldn't? I think it does.
Perhaps one last point in this stream of thoughts: The Apostle Paul teaches us that we receive a new heart and become a new creature in Christ. It seems to me that the idea is that the old, deceivable one gets replaced with a new and more immunized one. "...they had no more disposition to do evil..." was the phrase used to describe the state of being in which the Nephites found themselves after King Benjamin's discourse.
What would change in you if you saw the Atonement as a railing in addition to an ambulance? "Permission" and well as "forgiveness"?