In Luke 19:9-10, Jesus said to Zacchaeus, “Today salvation has come to this house, because this man, too, is a son of Abraham. For the Son of Man came to seek and to save the lost.” Zacchaeus clearly showed signs of repentance (v.8). Jesus didn't say salvation would come to his house in one week or in one year -- but "today."
     It was the same with the house of Cornelius in Acts 10, and Lydia Acts 16, and the jailer in Acts 16. Not to mention the 3000 souls in Acts 2 -- or the Ethiopian in Acts 8. Moreover, in 2 Cor 6:1-2, Paul said "Now is the day of salvation." Thus it is the obligation of the church to teach against the widespread distortion of this truth. The earlier believers were baptized on the same day they received the gospel. -- a Ghanaian brother
Thanks for the question. Sure, I have heard the idea before, but not the doctrine -- with the possible implication that those who do not agree with this view are false teachers. Let me take the examples in order.
  • Zacchaeus: For all we know, he was a Jew who had wandered from the covenant, who was getting his life right with the Lord again. The Spirit, an integral part of being a Christian (Rom 8:9) wasn't given until Jesus was glorified (John 7:39) -- s0 Zacchaeus was being restored to the old covenant. Strictly speaking, no one became a Christian in the gospels. That is, in the first 90 chapters of the NT (Matt 1-Acts 1) God's covenant people are Jews. The new covenant, made possible by Jesus' death, resurrection, and ascension, went into effect at Pentecost (Acts 2). In short, Zacchaeus did not become a Christian in Luke 19 (though we certainly presume he stayed with the Lord even after the day of Pentecost). So we need to be careful to distinguish the two covenants. Much confusion has resulted from a failure to understand the covenants.
  • Cornelius: Yes, he and his family and friends (Acts 10:24) were baptized the very day they heard the message. Which was after they had experienced the preaching of an apostle and a miracle. Not only that, but they had been selected because they were Gentiles. Acts carefully shows us the progress of the gospel from the Jews to the Samaritans to the Gentiles (Acts 1:8--an important verse!). The significance of the case of Cornelius is not what he experienced or his particular conversion, but of his role in salvation history. 
  • Lydia: Paul's missionary pattern was to enter a city, seek the synagogue, and begin preaching the good news there. Philippi was a Roman colony, apparently without a synagogue. In lieu of a synagogue, it was customary to gather at rivers. In other words, Paul expected to find those already attracted to the true God, Jews as well as Gentiles, at the river. And that is just what happened.  This means it is misleading to imply that one day Lydia knew nothing of God and this Word, and the next day she learned everything and became a Christian. We simply don't know how many years she had been studying the scriptures!
  • Jailer: Of all the examples you mentioned, this most supports your point. There is no indication that this Roman was familiar with the gospel, though we simply don't know what "head start" he may have had spiritually. So I think it is fair to concede this conversion as a one-day event. (Or one-night event, if you want to be picky.)
  • Pentecost group: These guys had received up to three years of teaching before they went into the water! They already knew who Jesus was (Acts 2:22). And they had just witnessed miracles. Considering their extensive preparation, it would be disingenuous to highlight this crowd as "first-timers." (For more on this, please listen to my podcast “Surprises from Acts 2.” Consult also the 22 March 2017 newsletter, where we learn that the group wasn't 3000, but probably much larger.)
  • Ethiopian: This man was just returning from Jerusalem, presumably to attend one of the three great feasts (Passover, Pentecost, or Tabernacles). He was so hungry for the truth that he was reading the scriptures when Philip met him! He is a good example of what the NT calls a "god fearer." These were Gentiles who were attracted to the purity and wisdom of the Jewish religion, yet hesitated to take the final step of circumcision (impossible in the Eunuch's case anyway). Like Cornelius (Acts 10:2), this god fearer had been well prepared for his rendezvous with Philip. So I find nothing noteworthy in his same-day baptism. What is more surprising is that he went on his merry way -- not back to Jerusalem to plug into one of the house churches or other Christian gatherings -- but back to Africa, and without a mentor. However, given his likely pattern of visiting Jerusalem, this man may be presumed to have returned to the mother church with some regularity.

And now, back, to your view of "the day of salvation." I would hold that “today” isn’t so much a chronological period as a key theological moment in salvation history. That is, the Day of the Lord was dawning. God has drawn near. In the Bible “day” is often used, not in the sense of 24 hours, but in the sense of a crucial epoch or important point in time. (The first instance is Gen 2:4: "These are the generations of the heavens and the earth in the day they were created.")

Considering the failure of the examples above to prove that one-day conversions were the norm, I would suggest you be less dogmatic about your view. Yes, some men and women become Christians in a single day. Most of these already have significant Christian background experience, though not all, and there's nothing wrong in principle with people responding to the message the very first day they have inclined their hearts to God. However, in our messed-up world, it often takes considerably longer.

Your question does raise an important point. We should not make it difficult for those who are turning to God. Please consider a few final passages.

  • "But woe to you, scribes and Pharisees, hypocrites! For you lock people out of the kingdom of heaven. For you do not go in yourselves, and when others are going in, you stop them" (Matt 23:12). (Stick with the scriptures; don't pile up extra rules and regulations. When we do, it becomes difficult to distinguish God's word from our own!)
  • "... We should not make it difficult for those Gentiles who are turning to God" (Acts 15:10). (Streamline the teaching process -- James's wise counsel still applies today.
  • The fundamental doctrines of the faith are simple. Let's proclaim the one body, one Spirit, one hope, one Lord, one faith, one baptism, and one God (Eph 4:4-6), so that our hearers may leave sin behind as quickly as possible, embracing the new life. Speaking of how the lost were "learning Christ," Paul wrote "Surely you have heard about him and were taught in him, as truth is in Jesus. You were taught to put away your former way of life, your old self, corrupt and deluded by its lusts, and to be renewed in the spirit of your minds, and to clothe yourselves with the new self, created according to the likeness of God in true righteousness and holiness." (Eph 2:20, 21-24).

Whether or not that means we should see more one-day baptisms, I cannot say. Maybe so.