"‘...As I live!’ declares the Lord God, ‘I take no pleasure in the death of the wicked..." Ezekiel 33:11 NASB
It is quite clear from scripture that there is a place of eternal judgment and that it will be populated with unsaved sinners as well as the demon horde. Eternal confinement to a lake that burns with fire seems harsh, minimally--not at all the kind of thing one might anticipate someone styled "Savior" doing. I think it would be natural to think that God would have done something about that, if he could have.
"...I urge that entreaties and prayers, petitions and thanksgivings, be made on behalf of all men, for kings and all who are in authority, so that we may lead a tranquil and quiet life in all godliness and dignity. This is good and acceptable in the sight of God our Savior, who desires all men to be saved and to come to the knowledge of the truth. For there is one God, and one mediator also between God and men, the man Christ Jesus, who gave Himself as a ransom for all..." 1 Timothy 2:1-6 NASB
It seems to me, what God could do to save all humanity from judgment he did do. If all humanity does not end up saved, the fault will not lie with God, but with man. He has provided a substitutionary sacrifice for sin that effectively meets the demand that both man and God see for justice, and effectively reconciles the broken relationship between God and man the sinner. All that is left is for man to no longer want to be a sinner.
Now that is not something that can be imposed. It can be coaxed, an invitation can be made, and a supernatural effort to convince the sinner of his perilous status can be undertaken. But to write over the will of the person in order to make it happen would only serve to cause the sinner to cease being a man. The result could not be said to be a man being saved, but would represent a man being transformed into something other than a man, something less than the image of God.
Man was made in the image of God, to do as he pleased. A man could not be said to be a man on those terms if someone else's pleasure were substituted (especially unwillingly) for his own. To be a man is to have independent will. Unfortunately, it is also to have the possibility of withstanding every effort of God to turn that will to the obedience of faith.
Is there a person God cannot save? Yes, the one who won't repent and believe the gospel.