Sooner or later, if the subject sinner shows no true repentance, "turning away" by definition, then Christ will take his hand off or your shoulder, and allow you to keep on sinning, and without remorse. God loves us infinitely, and if we don't want to accept the sacrifice he will not force it on us. He will tearfully allow us to go down the road to perdition with great hope of his child turning away from sin before his mortal life is over. There is great rejoicing in heaven when even one lost soul comes back to the fold.
I've often wondered if it's akin to God hardening Pharoes heart, so that he would not let the Jews out of their bonds of slavery. Surely he loved Egyptians as much as anyone else. Surely he didn't ordain that Pharoe be in hell. But it seems to be what Pharoe wanted, so God granted him is autonomy and freedom.
There is hell. In spite of God's endless mercy, and love. Without a choice for his creatures, (which includes Angels, of whom he lost 1/3), to choose not to love Him enough to valiantly work to turn away from sin, then He must grant them their wish to remain outside of His ways, and His will for us. Without hell, there can be no Heaven. There can be nothing to turn away FROM, and nothing to turn TO.
God IS love. And those who love God, because of Jesus cross, may live in love for eternity. Without the cross, this option would not be left to any of us, except Jews who remained deeply orthodox and stuck to the letter of the written law. With Christ, the law was written on our hearts. We now have the ability to know what is good and bad without the law. But the law itself has never changed. Only the penalties inflicted by MAN against MAN for breaking the laws. We now know what is fitting and right by grace. Grace came to us through Jesus Christ.
So, no, Jesus blood is in no way insufficient, and we should be ever thankful that it was shed for many for the forgiveness of sins. Without it, we wouldn't even have a shot at Heaven, because we would otherwise need to "be perfect, as our Father in Heaven is perfect". Jesus died for us, and continues to pray for us. He and our angels are always pleading our case to the Father. All we need do is love the Father, and believe on Jesus Christ. We show this by our repenting of our sins. Since repenting is "turning away", this means even when we fall, we get up, dust ourselves off, and do our dilligent best to not sin again. "Then neither to I accuse you. Go and SIN NO MORE". But being fallen by nature, we likely will sin again. This is why, by his grace, He gave the Apostles, by the power of the Holy Spirit the power to bind and loose on earth, and gave us successors to the Apostles to loose of from those sins for which we are truly repentant. The ability to do penance for our sins, and as long as we keep ourselves in the process, not only will He never take His hand off our shoulder, but we can actually see a diminishing of temptation over time to the point, (by the grace of God), that even our most repetitive sins, have been reduced dramatically, and that when they occur, our remorse is relentless in returning us to God for forgiveness when we fall.
God bless,
Steven