Regarding the beliefs of John Calvin, Stanley M. Burgess informs us:
"At the fall, however, the natural gifts present in humans were corrupted, and the supernatural gifts were removed. Because humans are now despoiled of the Spirit's gifts, and of the 'light of reason, justice and rectitude,' they are prone to every evil. No longer considered worthy to be guided by the Holy Spirit, humans are abandoned to Satan's actions" (Burgess 3:164).
Calvin himself asserted the following:
"we do not condemn those inclinations which God so engraved upon the character of man at his first creation, that they were eradicable only with humanity itself, but only those bold and unbridled impulses which contend against God's control" (Institutes 3.3.12).
Granted, I'm not sure that Calvin explicitly affirms that the IMAGO DEI in man was lost at the Fall. Nevertheless, he writes that the IMAGO DEI of infralapsarian humanity was so distorted at the Fall that the human mind "conceives, desires, and undertakes, only that which is impious, perverted, foul, impure, and infamous. The heart is so steeped in the poison of sin, that it can breathe out nothing but a loathsome stench. But if some men occasionally make a show of good, their minds nevertheless ever remain enveloped in hypocrisy and deceitful craft, and their hearts bound by inner perversity" (Institutes 2.5.19).
Based on these Calvinistic ideas, I would say that positing a nature/supernature dichotomy in this way does nothing to advance our understanding of human nature from a scriptural viewpoint. Calvin had a pretty dim view of fallen man qua fallen man. This is not to say that man is "basically good" as Enlightenment thinkers generally claim since we are sinners by nature (Romans 3:23). But I cannot concur with Calvin when he asserts that humanity only conceives what is vile and wicked. Nor can I agree when he claims that "some men occasionally make a show of good," but their hearts are still filled with malice and inner perversity; this evaluation goes wholly against the apostolic teaching of the "law within" (Romans 2:14-15). Some people without law do by nature the things of the law; yet there are also other consequences that are concomitant with his teaching.
(1) The teaching of total depravity indicates that man has absolutely nothing to do with his salvation: "Someone may say, 'Yes, the Holy Spirit must draw us to God, but we can use our freedom to resist or accept that drawing.' Our answer is: except for the continual exertion of saving grace, we will always use our freedom to resist God. That is what it means to be 'unable to submit to God.' If a person becomes humble enough to submit to God it is because God has given that person a new, humble nature" (John Piper). See http://www.desiringgod.org/articles/what-we-believe-about-the-five-points-of-calvinism
Of course, we might all agree that God is the Savior--the initiator and sole Director of the marvelous soteriological process. Yet the part that a human plays in salvation is a point of separation for many theologians. Luther defined faith in terms of FIDUCIA ("absolute trust in God"). He believed that faith is a passive act of reception in which we only receive God's grace. But as Emil Brunner has aptly pointed out, the dynamics of salvation cannot be explained properly in terms of cause and effect (divine activity and human passivity): it is much better to view salvation as a process of action and reaction insofar as God acts while man reacts. If what Brunner says is true, then it seems that we too play a significant part in our salvation (Philippians 2:12). We evidently have the ability and intellectual power to act in response to God's invitation and make important changes that show our love for God and the good news about Christ. It is not just a matter of God giving and our passively receiving. None of what I say here, however, is designed to minimize the role that God's spirit plays in shaping or directing our wills. God does indeed empower us to make changes in our lives--to receive his Son as the pioneer and high priest of our salvation.
(2) Total depravity also clouds the truthfulness of passages like Mark 10:18. While it might be tempting to understand this verse as a claim to Deity by Jesus Christ, in actuality, the verse is simply declaring that God is the only one who is superlatively Good. I.e., Jehovah is the only One who measures up fully to the absolute standard of goodness. This truth can be easily demonstrated by cross-referencing Revelation 15:1-4 and 1 Samuel 2:2. The account in Revelation says that only God is holy. Yet 1 Samuel 2:2 says that no one can compare with God in holiness. The verses are not contradictory: Revelation 15:1-4 is simply demonstrating the superlative nature of God's holiness. This point is also illustrated by the many examples in both the OT and NT that declare men and angels to be holy.
Lastly, I would acquiesce with the claim that man can do nothing on his own regarding his salvation: we all need the holy spirit to turn from lives of sin to lives of righteousness (1 Corinthians 6:9-11). However, there is an interesting tension at work between God guiding us (not coercing us) to believe in him and our taking the initiative to form intentions to serve him. Again, I refer to the law within and Joshua 24:15 which indicates that we must make the choice to serve or reject Jehovah. Making that choice of our own volition would be impossible if Calvin's words were true.