They are commonly called Pelagians. (and in the sense that Pelagius was only a semi-Pelagian at worst, I think it could be said that they are (FR5th)-Pelagians)as well.
They are those who think that a man can somehow stumble upon salvation by faith without the leading of the Holy Spirit.
Have the various factions agreed on a definition of (fr5th)-Calvinism yet? The thread is a bit difficult to follow and I had a long day.
Be careful. I've been going through a number of Charles Finney's sermons and you've just describe his message.