Jn. 8 is in a context of Jesus talking to the hard-hearted Pharisees. They are being rebuked as children of the devil. They do not love God, they are not of God, and they do not have ears to hear.
We concur that they are spiritually dead. If they would have believed His testimony (which they did not, even in the face of miracles), and been WILLING (even if not able to on their own) to repent and obey, God could have and would have saved them. With the hard-hearted He preached judgment. Their are many other examples with the broken and open people where Jesus just had to say: Come, follow me; Go, and sin no more; remember me= Today you will be with me in paradise. A mustard seed of faith resulted in transformation from the kingdom of Self/darkness to the Kingdom of God.
Jn. 8 is not a proof passage for Total Depravity. It is specifically dealing with willfully blind and deaf religious people who ultimately crucified Christ. There were Pharisees that did believe. Nicodemus was an example (Jn. 3). Is it that he was chosen from eternity as one of the 'elect' and the others were chosen to demonstrate God's wrath (predestined to hell even if they would have liked to follow Christ)? Nicodemus had a different heart than most Pharisees. He sought the Lord out and wanted to understand spiritual truth. Jesus gave him more light that changed him, rather than hardened him. He did not blaspheme God and His works like the other Pharisees did. There is nothing implicit in Scripture to think that this was because of predestination and election. It seems to be a matter of hunger or hatred for the Living God. There is no good reason why God would not draw all men to Himself and impartially love everyone equally. There is no reason to think the atonement was only intended for those God elected before birth. It is comprehensible that the atonement is for the whole world, yet not everyone will be willing to hear and obey His voice. The Pharisees did hear the truth of the Messiah, but they refused to trust Him.
My rejection of Total Depravity does not mean that it is easy to repent and obey. We have physical depravity that makes it difficult to not live for self and the flesh. It is not a vertical mountain impossible to climb, not is it a flat plane that makes it easy. There is a steep grade and left to ourselves we do not seek God nor walk in the Spirit. I do not believe we have moral depravity as a fetus since sin is a wrong moral choice/lawlessness, not a physical, inherited substance.
So when the truth of God hits us, we can plug our ears and continue in sin, or we can take steps toward seeking God. He initiates, he draws, he enables (which is not coercive). When we say in simplicity and child-like faith: Just as I am I come...have mercy on men a sinner...the King of the universe floods into our lives transforming us and enabling genuine repentance and faith. If we harden our heart on the day of salvation, we are warned about the consequences of unbelief (Hebrews).
I affirm that we cannot save ourselves. I disagree that it is not innate to want to know the Creator. I disagree that God only wants to save a few in a holy huddle independent of our wills. Repentance and faith are not works. They are not done by God, but God frees us up to do so if we will hear and obey His voice and conviction. If we hear but disobey, His voice and conviction will wane eventually. We are without excuse, nor is God to blame for those who are lost.
So, do we passively wait for God to save the elect? The Calvinists in the 1900s did that and they were a dead group among dying men.
Evangelist Charles G. Finney was powerfully transformed as he submitted to God's conviction and call. He saw dead men swept into the kingdom in New York as he preached the character and attributes of God and the law of God as a schoolmaster. He assumed from Scripture that God wanted to save all those who would hear and obey the truth preached in the power of the Spirit and authority of the Word. He fulfilled the Great Commission and saw people come to Christ (will, intellect, not primarily emotion as you would accuse him). Unlike today, a high percentage of people remained disciples. He did not preach 'easy believism'.
How to preach the Gospel:
"We should present to their minds the character of God, his government, Christ, the Holy Spirit, the plan of salvation, any such thing that is calculated to charm the sinner away from his sins, and from pursuing his own interests, and that is calculated to excite him to disinterested (unselfish) and universal love. On the other hand, his own deformity, selfishness, self-will, pride, ambition, enmity, lusts, guilt, loathsomeness, hatefulness, spiritual death, dependence, its nature and extent; all these things should be brought to bear in a burning focus on his mind. Right over against his own selfishness, enmity, self-will, and loathsome depravity, should be set the disinterestedness (unselfish), the great love, the infinite compassion, the meekness, the condescension, purity, holiness, truthfulness, and justice of the blessed God. THESE SHOULD BE HELD BEFORE HIM LIKE A MIRROR UNTIL THEY PRESS ON HIM WITH SUCH MOUNTAIN WEIGHT AS TO BREAK HIS HEART."
The Spirit uses the foolishness of preaching Christ and Him crucified to convict, convince, and convert. Jesus and Paul preached this way revealing the love and holiness of God in contrast to the sinfulness of man. So should the church today, rather than waiting for God to write in the sky. There is no passion and urgency to preach the Gospel if everyone's destinies are fixed as the lucky 'elect' or the loser non-elect. It is all of God and nothing of man...or is it? He commands men everywhere to repent. He commands us to be born again. These are not optional suggestions. God would not tell us to repent or come to Him to have life if we were 'dead' to the point we could not even cry out for mercy in response to His love and conviction. This is a simple act of the will and mind (child like faith we are exhorted to).