Is everyone or are only some “drawn” by the Holy Spirit?
First, I think that there is an element of mystery here, and that we will never be able to “put God in a box” to the degree that we have all our questions answered, with all tensions or apparent contradictions resolved. Here, the issue is the sovereignty of God and the responsibility of man. I believe that God is sovereign, without qualification. I also believe that man is responsible. Hell is not just a place for God's rejects, it is a place for those who have chosen to rebel against God, and to reject His offer of salvation in Christ.
There are those who define God's “foreknowledge” as His knowledge of what men will do in the future, and specifically (so far as this discussion goes) His knowledge of whether or not we will choose to believe in Him. Those who would minimize God's sovereignty and emphasize man's responsibility would say, “God looked down through the corridors of time, saw those who would trust in Him, and then chose them for salvation. There are several problems with this position, however. First, it does not fit the statements of (for example) John, Acts, or Romans concerning man's depravity and God's sovereignty. This explanation does not square with the fact that unbelievers are “dead in their trespasses and sins,” who are born in sin, opposed to God, and who neither seek God nor understand spiritual realities (Romans 3, Ephesians 2:1f., 1 Corinthians 2). In other words, if God looked down through the corridors of time to see who would believe in Him (apart from His prior choice of choosing, illuminating, calling), He would see no one. There is none who seeks God (Romans 3:11). Second, the position stated above would make man the first cause of salvation, not God. God would be choosing only those who first chose Him. To change terminology for a moment, we are told that we love God because He first loved us (1 John 4:19). I think it is also true of faith. We have faith in God because He gives it to us. God is the first cause of our salvation. That truth is rock solid, in my opinion, and this is the very premise that should give us hope and comfort:
NAS Philippians 1:6 For I am confident of this very thing, that He who began a good work in you will perfect it until the day of Christ Jesus.
In answer to your question as to how many (all, or just some) are drawn, I think that the answer is quite clear:
NIV Matthew 22:14 “For many are invited, but few are chosen.”
NAS Matthew 22:14 “For many are called, but few are chosen.”
29 For whom He foreknew, He also predestined to become conformed to the image of His Son, that He might be the first-born among many brethren; 30 and whom He predestined, these He also called; and whom He called, these He also justified; and whom He justified, these He also glorified (Romans 8:29-30, NAS).
I see no dropouts here. Those whom God foreknew, He predestined, and He called, justified, and glorified.
48 And when the Gentiles heard this, they began rejoicing and glorifying the word of the Lord; and as many as had been appointed to eternal life believed (Acts 13:48).
In Acts 16:14 it is very clear that God opened Lydia's heart, so that she was able to respond to the gospel:
And a certain woman named Lydia, from the city of Thyatira, a seller of purple fabrics, a worshiper of God, was listening; and the Lord opened her heart to respond to the things spoken by Paul (Acts 16:14, NAS).
I think one has to conclude that salvation is of the Lord, that it is He who first chooses, He who enlightens, He who calls. All those whom He has chosen come to Him.
But having said this, I see a strong sense of invitation, even urging, that men should believe. Men do have a choice to make, and they will be held accountable for it, eternally. So let us not set aside this other side of the matter: Notice how this text includes both sides (invitation/responsibility and sovereignty):
23 “And you, Capernaum, will not be exalted to heaven, will you? You shall descend to Hades; for if the miracles had occurred in Sodom which occurred in you, it would have remained to this day. 24 “Nevertheless I say to you that it shall be more tolerable for the land of Sodom in the day of judgment, than for you.” 25 At that time Jesus answered and said, “I praise Thee, O Father, Lord of heaven and earth, that Thou didst hide these things from the wise and intelligent and didst reveal them to babes. 26 “Yes, Father, for thus it was well-pleasing in Thy sight. 27 “All things have been handed over to Me by My Father; and no one knows the Son, except the Father; nor does anyone know the Father, except the Son, and anyone to whom the Son wills to reveal Him. 28 “Come to Me, all who are weary and heavy-laden, and I will give you rest. 29 “Take My yoke upon you, and learn from Me, for I am gentle and humble in heart; and you shall find rest for your souls. 30 “For My yoke is easy, and My load is light” (Matthew 11:23-30).
The biggest problem I see is that in trying to prove or defend one side of the equation, we are tempted to minimize the other. The Bible proclaims both, and thus so should we.