Lots of stuff to comment on in this thread, yet another excellent one from Jesusfan.
Is the Bible (or the Bible's message, the Gospel of Christ) the chosen means God uses to regenerate the elect? No. First regenerate means again originate, so when we are conceived in Adam, we are spiritually dead, separated from God. When God puts us spiritually in Christ, we are made alive (regenerated/born again) together with Christ. No one is regenerated or made alive outside of Christ. So the chosen means, and BTW what an apt characterization, is for God to spiritually place us in Christ, thus we are individually chosen and placed in the Chosen One.
Faith comes from hearing and embracing God's revelation. So the revealing grace, including the Gospel and all the mechanisms used to cultivate us, plant us and water us, is a gift from God, but it does not "enable" as in modify our attributes supernaturally so we can receive it. That is fiction with no scriptural support. But no one is saved by trusting in Christ, because we do not save ourselves, it is God who credits our faith, as worthless as it may well be on and by itself, as righteousness and places us spiritually in Christ. God does it all, except for our autonomous choice to trust and rely on Jesus.
Of course the gospel is the power of God to salvation, Romans 1:16 says (NASB) "For I am not ashamed of the gospel, for it is the power of God for salvation to everyone who believes, to the Jew first and also to the Greek. Note it does not cause belief, but it does provide the revelation enabling someone to chose to embrace it with all their heart, or something less, or even reject it. See Matthew 13:1-26
Would a person have to be "regenerated" or supernaturally altered to enable the person to receive the gospel? No, 1 Corinthians 3:1-3 says "men of the flesh" can receive the milk of the gospel, and that is how Paul addressed the "babes in Christ" who had not learned enough with the aid of their indwelt Spirit to be able to handle spiritual meat.
The problem with 1 Corinthians 2:14 is people do not look at the context including chapter 3. It says "spiritual things" and does not say either "all spiritual things" or "some spiritual things." But from the context, Paul meant "some" spiritual things, the things discerned with the aid of the indwelt Spirit, because without the Spirit they are unable to understand them. But the milk of the gospel, Chapter three, can be understood by men of the flesh.
Doesn't this show a person has to be "quickened" which is just an old fashioned word for being made alive. Calvinists us quicken as if it happens before a person receives the gospel fully, but quicken simply says to be made alive together with Christ.
If you take a careful look at John 1:10-12 you will see the sequence laid out with perfect clarity:
12 But as many as received Him, to them He gave the right to become children of God, even to those who believe in His name,
13 who were born, not of blood nor of the will of the flesh nor of the will of man, but of God.
First we must receive Him. But who decides whether or not we did in deed receive Him. Romans 4:5 answers that question, God decides whether we did or not to His satisfaction and then credits our dirty rag faith as righteousness. So trusting in Christ did not "put us in Christ" or earn a place in Christ. God has mercy on whom He has mercy and it does not depend on the person who wills to be saved. Romans 9.
What did God do? He gave them the "right" to become children of God. Note this does not say they became children of God. In context, our physical adoption as sons is in view and therefore we are given the right to be physically adopted as sons at the second coming. And how was this "right" given? God put us spiritually in Christ and sealed us with the Holy Spirit as a pledge for our inheritance of eternal life as children of God. So the sequence is we believe in His name, God credits it or not, as righteousness, then He places us spiritually in Christ, where we undergo the circumcision of Christ and arise in Christ a new creation. And how were these new creations born? Not of blood, nor the will of the flesh, nor the will of man, but of God. The gospel of Christ.
lol