Hi Rookie,
In Psalm 119:35-36 we read:
Make me to go in the path of thy commandments; for therein do I delight. Incline my heart unto thy testimonies, and not to covetousness.
Here we have the Psalmist delighting in the law after the inward man (if I may turn a phrase), but asking God to show him how to perform what is written. In my view this was Paul's testimony prior to being Born Again. He goes on to say, " Incline my heart unto thy testimonies, and not to covetousness. " By inference, his heart was not rightly inclined. This is the pattern of the Old Covenant. The saints thereof were a remnant people; but that must not be confused with what is available under the New Covenant. In fact, as great a man as John the Baptist was, he that is least in the Kingdom of Heaven would be greater than he. How can this be? John the Baptist preached a kingdom that he, himself, was not yet in. That is the plain reading of the text. It was at hand (Matthew 3:2), but it was not yet.
The law and the prophets were until John: since that time the kingdom of God is preached, and every man presseth into it. (Luke 16:16)
Jesus answered and said unto him, Verily, verily, I say unto thee, Except a man be born again, he cannot see the kingdom of God. (John 3:3)
Jesus answered, Verily, verily, I say unto thee, Except a man be born of water and of the Spirit, he cannot enter into the kingdom of God. (John 3:5)
Based upon what your conception of Zac Poonen's teaching, I find what he is saying to be wholly true. John the Baptist announced the arrival of the Kingdom. This signaled the time of preparation for the coming of Messiah who would eventually lead to the possibility of a radical change in the nature of fallen men and women. The Old Testament is loaded with pictures of what God would do in the New Covenant. This includes a new heart and a new spirit.
Perhaps most importantly, the New Covenant creates a new race of men who are Born Again in Christ. We are in Adam by first birth and suffer all that his sin caused in the fall. You are aware of the teaching of original sin, so I will not expound. When Jesus told Nicodemas in John 3:3 that "you must be Born Again (born from above)" He was offering a possibility never before known to man. We were born by first birth in Adam; we are born again by New Birth into Jesus Christ, the last Adam.
In the same way that being in Adam effected mankind for evil; being born again into Jesus Christ affects us to the nature of the last Adam. As natural as it was to sin in Adam, it is natural to do righteousness for those in Christ. This was never available prior to Christ's death. Why? It was New. How could a person be "in Christ" whilst Christ walked the earth? How could they be baptized into His death when He had not died to Sin yet Himself? Our death to Sin, our being raised with Him, etc. are all aspects of the New Covenant. Nobody was in the New Covenant prior to Pentecost. It is impossible. It had not been made effectual or available.
Jesus is the one who spoke of the hardness of hearts. Zac Poonen is only taking up His claims. But this is only a portion of the story. They were of their father the Devil and the lusts of their father they did do. This was the problem with man. It is the diagnosis. (1 John 3:8-3:10) The Old Covenant could do nothing more than impose upon the people an institutional type law, with a view to correcting their behavior under the Adamic nature. It exposed their sinful nature, and quantified their sin. It made them very sin conscious. The Law was Spiritual, but men were carnal and sold under Sin. One cannot do with institutional law what can only be done by a change in a one's constitutional nature. It was a stop-gap measure until the Seed came to whom the promises were made (Galatians 3:19). These promises have been passed to us that we might be partakers of the Divine Nature. They were not given to those in the Old Covenant. This is the promise of the New Covenant.
I can send my dog to obedience school, and he may come home and act more civilized; but this is not a change of nature, it is the imposition of institutional law upon him. This is what the Old Covenant did for those under it. Nevertheless, God is bringing many sons unto glory. Prior to being born again, all have sinned and fallen short of the glory of God. Man has always fallen short of the glory of God, no matter how great he or she was. however, God is bringing many sons unto glory through the New Covenant. In Christ, the saying is fulfilled, "Let Us make man in our own image and likeness..." God wants children who partake of His Divine Nature. Not His omnipotence, omniscience, etc.; but His personality and character. This is what the New Covenant provides. It is New. It became available at Pentecost. It enabled mankind who had been born after the generations of Adam to be born again into the generation of Jesus Christ.