Romans 10:13 says: For whosoever shall call upon the name of the Lord shall be saved.
There is no grey area there. The problem (as I see it) are those who wait until the last minute to accept Jesus. I have heard folks say "I'll take care of the God thing before I die." We have no certain promise of our next breath. Those fortunate enough to have a "death bed" exit from this world and time to accept Jesus are "lucky." Those lives that are taken in an instant (I assume) have no time to call upon the name of Jesus.
And another thought to your comment is that we do not get saved when we want to. We are saved by the pulling and convicting power of the Holy Spirit and if He is not doing that then it is impossible to be saved. That is why Paul said that "TODAY is the day of salvation"!