Permit me to suggest the following answer as I currently see it.
Historic Calvinists (I believe) regard repentance and faith as the means by which the great commandment to love God and love our neighbor finds fulfillment. This "duty" to love God and neighbor existed before the fall and Adam certainly enjoyed the ability to do so. Our love of God is therefore still obligatory, and the means through which it is to be realized, namely repentance and faith, are likewise obligatory. We owe God our love and trust by the very fact that we are His rational creatures. Adam had the ability to love and trust God before the Fall. We are still responsible to love and trust God even though, because of the Fall and while in our unregenerate state, we do not have the ability to do so. Therefore, fallen man is indeed duty-bound to repent and believe in Christ for salvation -- even though left to himself he is unable. Biblically speaking, responsibility to God does not imply or necessitate ability on our part.
Yet, the basis and motive for the gospel call is not man's duty, but the grace of God in Christ.
Having said that, I am open to critique and correction. I have viewed the "denial of duty faith" as a characteristic of hyper-Calvinism, as have Tom Nettles, David Engelsma, and others. However, I have also seen the idea of "duty faith" presented in a way that makes it seem wrong. So there are nuances in the discussion of the subject which may make it difficult or confusing.