God offers salvation to all, so in a real sense God does save sinners, but all one must do to be saved is to ask Jesus Christ into his/her heart. God desires that all be saved. It is not God who rejects a man, but it is man who rejects God.
Yes the Blood of Jesus was sufficient to pay the price of the sin of all mankind.....but we would agree that the atonement is limited to those that repent and turn from their sins..it is effective only for those that convert
Asking one into your heart is without effect unless you have repented first..God does not her the prayers of sinners..repentance MUST precede conversion..Repent and Believe
Mark 1:15 And saying, The time is fulfilled, and the kingdom of God is at hand: repent ye, and believe the gospel.
Luke 5:32 I came not to call the righteous, but sinners to repentance. Luke 13:5 I tell you, Nay: but, except ye repent, ye shall all likewise perish.
======================================
Saying a "sinners prayer " avails not...so we see here that He does not desire the unrepentant to be saved..He will not save them.
So we need to ask why do men reject the gospel.? That is a question that remains unanswered here
Ephesians 2
1 And you hath he quickened, who were dead in trespasses and sins; 2 Wherein in time past ye walked according to the course of this world, according to the prince of the power of the air, the spirit that now worketh in the children of disobedience:
3 Among whom also we all had our conversation in times past in the lusts of our flesh, fulfilling the desires of the flesh and of the mind; and were by nature the children of wrath, even as others.
4 But God, who is rich in mercy, for his great love wherewith he loved us,
5 Even when we were dead in sins, hath quickened us together with Christ, (by grace ye are saved;)
It is the Grace of God that brings repentance..why to some and not others?