No one ~ and certainly not John Calvin or any good Calvinist ~ denies that any man or woman makes a choice, and does so absolutely freely, of his or her own will and accord. Paul merely says it doesn't
depend on man's choice (his strength or willing), but rather on God, Who gives mercy and compassion to those whom He chooses to do so. It is not a matter of the will, but the heart, which drives the will, and what God does, in this mercy and compassion, changes the person's heart from stone to flesh, putting His Spirit into the hearts of those whom He chooses to do so. This is His salvific call.
As for the hardening of one's heart, Paul is crystal clear in Romans 9:18, that it is God who hardens:
"He has mercy on whomever He wills, and He hardens whomever He wills."
Ah, well let me ask you a question (rhetorical, really): If God knows beforehand (I'll talk about His foreknowledge in a moment) how people will respond ~ which He does, that's absolutely true ~ then, for those who He "knows beforehand" will respond negatively, why does He not do anything about it? <
smile>
Building upon what I said above ~ and I'll repeat here ~ it depends not on man's will, but on God's. Again:
"...it depends not on human will or exertion, but on God, Who has mercy... He has mercy on whomever He wills, and He hardens whomever He wills... Has the potter no right over the clay, to make out of the same lump one vessel for honorable use and another for dishonorable use? What if God, desiring to show His wrath and to make known His power, has endured with much patience vessels of wrath prepared for destruction, in order to make known the riches of His glory for vessels of mercy, which He has prepared beforehand for glory ~ even us whom He has called, not from the Jews only but also from the Gentiles?" (Romans 9:14-24)
And here's Paul again in Ephesians 1 (cited earlier):
"Blessed be the God and Father of our Lord Jesus Christ, Who has blessed us in Christ with every spiritual blessing in the heavenly places, even as He chose us in Him before the foundation of the world, that we should be holy and blameless before Him. In love He predestined us for adoption to Himself as sons through Jesus Christ, according to the purpose of His will, to the praise of His glorious grace, with which He has blessed us in the Beloved. In Him we have redemption through his blood, the forgiveness of our trespasses, according to the riches of His grace, which He lavished upon us, in all wisdom and insight making known to us the mystery of His will, according to His purpose, which He set forth in Christ as a plan for the fullness of time, to unite all things in him, things in heaven and things on earth. In Him we have obtained an inheritance, having been predestined according to the purpose of Him who works all things according to the counsel of His will, so that we who were the first to hope in Christ might be to the praise of his glory. In Him you also, when you heard the word of truth, the gospel of your salvation, and believed in Him, were sealed with the promised Holy Spirit, Who is the guarantee of our inheritance until we acquire possession of it, to the praise of His glory." (Ephesians 1:1-14)
No offense intended with this, certainly, but your use here of "drawing" is... very interesting. As I'm sure you know, Jesus Himself says, in John 6:44,
"No one can come to me unless the Father who sent me draws him. And I will raise him up on the last day." The opposite of what you say is true... He draws people ~ those whom He chooses, in His mercy and compassion to do so ~ to Himself, and in so doing softens their heart... changes the heart of stone into a heart of flesh, and thus it their God and they His people. This is His salvific call. This is exactly what Ezekiel, and Paul, and Peter say:
"I will sprinkle clean water on you, and you shall be clean from all your uncleannesses, and from all your idols I will cleanse you. And I will give you a new heart, and a new spirit I will put within you. And I will remove the heart of stone from your flesh and give you a heart of flesh. And I will put My Spirit within you, and cause you to walk in my statutes and be careful to obey my rules. You shall dwell in the land that I gave to your fathers, and you shall be my people, and I will be your God. And I will deliver you from all your uncleannesses" (Ezekiel 36:25-29).
"And you were dead in the trespasses and sins in which you once walked, following the course of this world, following the prince of the power of the air, the spirit that is now at work in the sons of disobedience ~ among whom we all once lived in the passions of our flesh, carrying out the desires of the body and the mind, and were by nature children of wrath, like the rest of mankind. But God, being rich in mercy, because of the great love with which He loved us, even when we were dead in our trespasses, made us alive together with Christ ~ by grace you have been saved ~ and raised us up with Him and seated us with Him in the heavenly places in Christ Jesus, so that in the coming ages He might show the immeasurable riches of His grace in kindness toward us in Christ Jesus. For by grace you have been saved through faith. And this is not your own doing; it is the gift of God, not a result of works, so that no one may boast. For we are His workmanship, created in Christ Jesus for good works, which God prepared beforehand, that we should walk in them" (Ephesians 2:1-10).
"Blessed be the God and Father of our Lord Jesus Christ! According to His great mercy, He has caused us to be born again to a living hope through the resurrection of Jesus Christ from the dead, to an inheritance that is imperishable, undefiled, and unfading, kept in heaven for you, who by God’s power are being guarded through faith for a salvation ready to be revealed in the last time" (1 Peter 1:3-5).
John says it, too:
"...to all who did receive Him, who believed in His name, he gave the right to become children of God, who were born, not of blood nor of the will of the flesh nor of the will of man, but of God." (John 1:12-13).
"We love because he first loved us." (1 John 4:19).
Now, regarding His call, and what depends on what... Listen to what the prophet Joel says. He's quoting God Himself here:
"...it shall come to pass that everyone who calls on the name of the Lord shall be saved. For in Mount Zion and in Jerusalem there shall be those who escape, as the Lord has said, and among the survivors shall be those whom the Lord calls" (Joel 2:32)
Notice what God says there, that
"For... among the survivors shall be those whom the Lord calls." That word 'for' there is very, very important; it is synonymous with 'because' in God's context there.
What follows that word 'for' indicates, irrefutably, that which what comes before that 'for' depends. As hard as it may be to digest or accept, our calling on His name ~ and thus being saved ~
depends first on our being called by the Lord.
Grace and peace to you.