What is man's responsibility for being saved? Does God require an obligation/choice to respond to the Gospel call - or do we have no choice or will in the matter and it is all preordained?

This is a very old debate - Calvinism vs Arminianism/Pelagianism is the technical theological label and you can read more about it by googling those terms.
Consider what the Bible says - Before God formed us in the womb, He knew us, and had a plan for us ( Jeremiah 1:5 ), the Spirit we have comes from Him ( Ecclesiastes - spirit returns to God who gave it 12:7)- and you will realize we are His creation, the sheep of his pasture.

For the saved - It is a joyous thing to consider that we are pre-chosen for Salvation. The absence of free will does not sting so much, because even if I had free will I would still want to go to heaven - duh - why would I want God to give me the ability to reject Heaven, and pick Hell instead ? And if I had free will, I would obviously pick heaven. Would picking hell be logical, smart or right? Of course not - like I said, Duh! So in one sense - free will or no free will, the outcome ( going to Heaven ) is the same - for the saved --whether you are a Calvinist or Arminian/Pelagian!

For the unsaved it's a different story, and it's the reason many others have a problem with Calvinism/Election. Here it would -seem- that even if the unsaved want to get into Heaven, they are prevented from making a free will choice to choose heaven. They seem to be preselected for Hell despite their interests and desires and never given a chance! They were picked to go to hell before they were born and that seems terrible and bad of God!

Paul had the same issue and question!!! Romans 9:14 What shall we say then? Is there unrighteousness with God? Certainly not! 15 For He says to Moses, "I will have mercy on whomever I will have mercy, and I will have compassion on whomever I will have compassion." 16 So then it is not of him who wills, nor of him who runs, but of God who shows mercy. 17 For the Scripture says to the Pharaoh, "For this very purpose I have raised you up, that I may show My power in you, and that My name may be declared in all the earth." 18 Therefore He has mercy on whom He wills, and whom He wills He hardens. 19 You will say to me then, "Why does He still find fault? For who has resisted His will?" 20 But indeed, O man, who are you to reply against God? Will the thing formed say to him who formed it, "Why have you made me like this?" 21 Does not the potter have power over the clay, from the same lump to make one vessel for honor and another for dishonor? 22 What if God, wanting to show His wrath and to make His power known, endured with much longsuffering the vessels of wrath prepared for destruction, 23 that He might make known the riches of His glory on the vessels of mercy, which He had prepared beforehand for glory, 24 even us whom He called, not of the Jews only, but also of the Gentiles?

You see dear friend, it's Gods universe. We have no right to question him. Paul does not have an answer other than to say it is not our place to question Him. Verses 20-22 are the key. He is saying trust God to save the righteous, and trust him to fry the truly wicked. He will save the right people, and there will be no one in hell that does not truly belong there.

We want God to play by our rules forgetting that He is the one who made us and the rules in the first place! So our focus on free will is really to give GOD a get out of jail free card - only those who choose to go to hell actually end up there - God has done everything he can by calling, preaching, knocking, so He is off the hook and it's man's responsibility.

It's the exact opposite! God is sovereign over His creation, and if anyone is going anyplace, its because He sends him there!Now you see Him for who he truly is. Awesome majestic terrible!

So what about free will and man's accountability?Think about it like this and this is really really the key question to ponder......

Why does one person respond to the gospel and another does not, when presented with the exact same evidence?Why does one person open the door to Jesus' knocking and another does not? Why?

Because they just don't feel like it? Because they are not intellectually convinced? Because the gospel is weak and foolish? Because there is something wrong with the way they were born, their environment, their circumstances, their upbringing and education, their theology, their age, their intelligence or lack of it, their situation? - what?

If being saved _ depends on all those stars aligning _ then it doesn't really depend on the will of the person, it's circumstance and accident that some get saved isn't it? What we call a _ free will choice_ then is merely a happy accident!

If God left us to our own devices, being saved would be accidental and coincidental, where is the justice, mercy, and love in that scenario? Now do you think it's more possible that God COULD align those stars on our behalf so that we DO make that free will choice to accept the Gospel. Yes, the decision was yours, but who led you to it? ------ So was it really your decision?  I think this lines up more clearly with scripture - God can bring about the outcome he desires without messing with man's free agency. He predicted/elected the crucifixion, but it was carried out by free moral agents acting of their own volition!

At the end of it all, I am thankful he picked you and me, and grateful he may save others if I pray for them. I am happy that all the stress is out of my hands, other than following his command to be a witness. I am happy to trust him with keeping me saved since I can't do it. And it gives me a better picture of how big and powerful and in control He is but also how intimately he is involved in everyone's life.

All Glory to Him !!!