Acts 19:1-7 has an interesting story that may have bearing on this:
1While Apollos was at Corinth, Paul took the road through the interior and arrived at Ephesus. There he found some disciples 2and asked them, “Did you receive the Holy Spirit when you believed?”
They answered, “No, we have not even heard that there is a Holy Spirit.”
3So Paul asked, “Then what baptism did you receive?”
“John’s baptism,” they replied.
4Paul said, “John’s baptism was a baptism of repentance. He told the people to believe in the one coming after him, that is, in Jesus.” 5On hearing this, they were baptized in the name of the Lord Jesus. 6When Paul placed his hands on them, the Holy Spirit came on them, and they spoke in tongues and prophesied. 7There were about twelve men in all.
Of interest here is the fact that John & Jesus preached the exact same same Gospel, so this was really, really close. The question is whether there is something magical about the syllables "G" and "Sus", which, especially bearing in mind that this wasn't originally in English, is unlikely.
What is more interesting is that clearly John's baptism was one of repentance - the very sine qua non of an altar call - and yet, clearly that's not enough.
What I surmise from this text is either:
(a) that inflowing of the Holy Spirit is therefore the choice of the Holy Spirit. While repentance was clearly a pre-requisite, it almost seems as though these people needed to accept the grace that the Spirit entails, even above and beyond repentance.
or (b) that it is in fact Jesus himself that is the key aspect of regeneration.