Alastair has a thoughtful post on Sinful Nature, Justification, Sanctification and the Spirit, well worth the time to read.
Christians are not to think of themselves as those with a fallen nature, but as those who have died to Sin. Such a way of speaking about our nature is a description of our nature as it appears to sight. The Scripture, I believe, speaks differently. For the Scripture our true nature is found in Christ. Whilst Christians certainly sin, when they do so they are living in conflict with their essential nature. Sin, whilst undoubtedly present in our lives, is a very much an alien and ‘unnatural’ presenceI wrote a post on sin a couple of months ago that has some similar ideas in it.