Dead varmits and weeding

This is kind of a truth re-visited, but yesterday God gave me two really appropriate illustrations of this truth. Let's just say that somewhere in your basement a dead varmint (mouse or piny squirrel) lies decomposing. The process is in the very early stages and the smell is permeating the house. What if we wake up every morning and spray the whole interior of the house with lemony-fresh air freshener? For a while it may smell better, but the lemony particles can only do so much and the stench of the varmint returns. The smell is sickening and cannot be ignored. The only solution is to find the culprit and remove it from the premises.
Sometimes when we're weeding the numerous flower beds around our home, the kids have a hard time removing the root of the weed they're pulling. Sometimes just the leaves come off, the stem snaps and the root is left there just waiting until we walk away to start growing again. For a day (or two if we're lucky), the flower bed looks great! But a cosmetic improvement just scratches the surface; we needed to go much deeper and rip out the root and all it's nasty tentacles.
So are we asking Jesus to forgive our sins (to be represented by the smell of the varmint and the leaves/stem of the weed) or are we asking Him to remove our sinful nature (like removing the dead rodent or ripping out the root)? It would be absurd to assign medications to a person based on their symptoms alone when the doctors know full well that cancer is the cause. Kill the cancer. Remove the varmint. Rip out the root.