Oh, golly, this topic has been beaten to death on this forum.
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However, it is worth repeating, so as to avoid unnecessary anxieties.
No, God does not exclude people from grace in order to satisfy His justice. Rather, people exclude themselves from grace by sinning, and God respects that choice. If they persist, they will experience at their death (the negative aspects of) God’s justice.
Grace is “efficacious” inasmuch as it gives us the capacity to do something we were unable to do before—namely, to love God in a supernatural way. It is also efficacious in the sense that, if we cooperate with God, it is He who brings us home—it is not we who bring ourselves home by our own efforts.
However, it is
not efficacious in the sense of
forcing us to love God—God wishes to respect our freedom.
The short answer: God gives efficacious grace to all men, without exception. (God desires the salvation of all men and gives them all the possibility of being saved, according to both 1 Tim. 2:4 and
Gaudium et Spes, 22.) However the efficacy of grace consists in making us
capable of loving God, not in
forcing us to love Him.
Why would God do this? Why not show forth all of His glory and hence make it impossible for us to refuse Him (as will be our condition in Heaven)? Because it gives us the possibliity of meriting something—to make hard decisions that will make us grow.