Forgive me, but I like to counter or at least balance this idea whenever I see it.
Another doctrine that hinders Gods work, and one which is heard almost everywhere, is that sinners are not lost because they have sinned, but because they have not accepted Jesus. Men are not lost because they murder; they are not sent to hell because they lie and steal and blaspheme; they are sent to hell because they reject a Saviour. This short-sighted preachment is thundered at us constantly, and is seldom challenged by the hearers.
A parallel argument would be hooted down as silly, but apparently no one notices it: That man with a cancer is dying, but it is not the cancer that is killing him; it is his failure to accept a cure. Is it not plain that the only reason the man would need a cure is that he is already marked for death by the cancer? The only reason I need a Saviour, in His capacity as Saviour, is that I am already marked for hell by the sins I have committed. Refusing to believe in Christ is a symptom of deeper evil in the life, of sins unconfessed and wicked ways unforsaken. The guilt lies in acts of sin; the proof of that guilt is seen in the rejection of the Savior.
If anyone should feel like brushing this aside as mere verbal sparring, let him first pause: the doctrine that the only damning sin is the rejection of Jesus is definitely a contributing cause of our present weakness and lack of moral grip... It is, for all its harmless seeming, a most injurious belief, for it destroys our sense of responsibility for our moral conduct. It robs all sin of its frightfulness and makes evil to consist in a mere technicality. And where sin is not cured power cannot flow.
- Paths to Power, A.W Tozer