God doesn't overlook our sin, He removes it in a process made possible by the suffering, death, and resurrection of Christ. We can't comprehend the horrific suffering of the heart of God as He watched His son die on a cross, agony He endured for the sole purpose of drawing us unto Himself.
It is a travesty to excuse continued sin with the logic that Jesus has already died and so we can't make things worse for Him by continuing to sin. In the first place, this logic is inaccurate because it is limited by our earth-bound perspective; all times are present to the Almighty God. He is above time and space, so that the death of the Savior is a current reality. How else could Christ have died for sins not yet committed?
We must not misunderstand the grace God extends to us. It is a grace that allows repeated cycles of failure, but it is not a grace that allows us to give up. We are not to say "what's the use?" or to give in to the status quo. We are not to continue in sin so that grace may abound.
Time and again we must come before the throne to say, "Father, forgive me."
But woe to us if we fail to come, fail to desire repentance and renewal, fail to acknowledge that sin that costs the death of Christ is anything but reprehensible. Sin has no redeeming qualities at all. Occasionally, as when a convicted criminal recently gave an interview for our local paper, someone will try to excuse wrongdoing with the argument that God brings good from evil. This man claimed that his crimes didn't really cause harm because God works everything to good (he'd held numerous people at gunpoint, and stolen thousands of dollars). He evidently doesn't know that Romans 3:7-8 says that anyone who speaks this way is condemned. This man's evil-tainted logic seems obvious to us, but we are in danger of the same kind of rationalization of sinful behaviors that seem too difficult to purge.
We must never give up; God forbid that we make peace with the sin that cost our Father God the death of His only begotten Son.
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What shall we say, then? Shall we go on sinning so that grace may increase? By no means! We are those who have died to sin; how can we live in it any longer? Or don’t you know that all of us who were baptized into Christ Jesus were baptized into his death? We were therefore buried with him through baptism into death in order that, just as Christ was raised from the dead through the glory of the Father, we too may live a new life.
For if we have been united with him in a death like his, we will certainly also be united with him in a resurrection like his. For we know that our old self was crucified with him so that the body ruled by sin might be done away with, that we should no longer be slaves to sin— because anyone who has died has been set free from sin.
Now if we died with Christ, we believe that we will also live with him. For we know that since Christ was raised from the dead, he cannot die again; death no longer has mastery over him. The death he died, he died to sin once for all; but the life he lives, he lives to God.
In the same way, count yourselves dead to sin but alive to God in Christ Jesus. Therefore do not let sin reign in your mortal body so that you obey its evil desires. Do not offer any part of yourself to sin as an instrument of wickedness, but rather offer yourselves to God as those who have been brought from death to life; and offer every part of yourself to him as an instrument of righteousness. For sin shall no longer be your master, because you are not under the law, but under grace.
--Romans 6:2-14