These words should not stand alone as a saving response to the Lord Jesus Christ. They shouldn't stand as the crucial, most practical point in a salvation presentation. As much as the phrase is used, one would think it must be located somewhere in Scripture. But it’s not. Neither the phrase or even the concept of “accept Jesus as your Saviour” is found in the Bible. “Saviour" is found 24 times in the NT. That might sound like a lot, but it isn't compared to the value that is being placed upon it in these anemic plans of salvation. Nor is it a lot in comparison to “Lord,” the title of Christ.
Though the terminology itself isn't found in the Bible, it’s pretty popular on the worldwide web, getting a few hundred thousand hits with that phrase, depending on the spelling of “Saviour.”
The term "Saviour" is found only 3 times in the gospels and twice in Acts. It is used more times in Titus (6) than those combined. And that's before we ever get to how the title "Saviour" is actually used. In its second usage, one of the very earliest in the gospels, Lk. 2:11 reads: "For unto you is born this day in the city of David a Saviour, which is Christ the Lord." “City of David” — think Davidic Covenant, then Saviour, who is Christ the Lord. He's the Lord, which would hearken to all those OT promises of the Lord, like Psalm 2:2, as one of many, many, many examples: "The kings of the earth set themselves, and the rulers take counsel together, against the LORD, and against his anointed." Lord is used three more times in Ps 2, more times than Saviour is used in all four gospels.
Of those 24 uses of "Saviour" in the NT, you get to the first in Acts (one of only two), and that reads: "Him hath God exalted with his right hand to be a Prince and a Saviour, for to give repentance to Israel, and forgiveness of sins." (Ac 5:31). If you were hearing this in that day, you might think to also "accept" Jesus as "Prince," since He’d risen from the dead and ascended to heaven, after hanging on a tree. He's coming back as Judge very soon, because he is "Prince," and you might have some time to turn to Him from your sins and self, to follow Him, and get forgiveness of sins, since He's Saviour.
Sure that's harder to say than "accept Jesus as your Saviour” but it gives a fuller picture.
If "accepting Jesus as your Saviour" were such important language, why doesn't it occur even once in the Bible? If the concept of "Saviour" in a salvation presentation were so important, then why didn't the apostles use it in their preaching?
Believe me, I’m all for using the title "Saviour," but definitely not in exclusion of "Lord" in the presentation of Jesus, and not even as the main point, since it isn't the main point.
Will He save? Yes. But He won't save while your mind is still made up that you're going to do whatever you want to do or that your religion is of some value or your sin is of some value or yourself is of value or your property is of some value or your family is of some value. And He doesn't become Saviour till He actually saves, since that is what the word means and all.
As you keep looking at the title "Saviour" in the NT, you'll see it used almost exclusively on behalf of believers, because Jesus is being described as their Saviour. But why is He their Saviour? Is it because they've accepted Him as Saviour? It doesn't say that. The tone of those passages is that He's been so good to them, as their Saviour, that they owe Him a lot. Saviour isn't being used in a presentation of salvation there. Four of the 24 times "Saviour" is found, it’s found in the following way (all in 2 Peter): "Lord and Saviour," Lord always coming first. Eight of the 24 “Saviour” verses, "Lord" is also found in the same verse. If we count "Prince" in Ac 5:31, that goes for 9 of 24. Even when "Saviour" is used, it gets used with "Lord" over one-third of the time. Wouldn’t you agree that Romans is the great salvation book? 45 times in 39 verses we find "Lord." 0 times we find "Saviour." As Paul explains the great doctrine of salvation so much in that book, he doesn't mention "Saviour" at all. Does this mean anything? Of course it does. You won't find "accept Jesus as your Saviour" in the book of Romans. You can't.
So in light of all this, why does this phrase appear as the clinching point or the finish line in so many plans of salvation for churches — in their tracts and on their websites and in their preaching?
In Rev 14:6 we have something preached by an angel, who flies around the earth so everyone can see him called the "everlasting gospel." It would be interesting, wouldn't it, to know what the everlasting gospel is? The next verse begins that everlasting gospel: “Fear God, and give glory to him; for the hour of his judgment is come: and worship him that made heaven, and earth, and the sea, and the fountains of waters."
Does anyone wonder why the angel doesn't just say, "Accept Jesus as your Saviour!!"? Perhaps he's talking to people who are already believers, since "fear God" and "worship him" are allegedly only sanctification concepts that can't be done until after someone is saved. Do we accuse the angel of preaching works salvation? Of course, I speak in jest. The angel is preaching the gospel and it’s not works.
If you want “Jesus as your Saviour,” your not going to get that by merely "asking Jesus to be your Saviour." If you don’t want Jesus as your Lord over all your life, Jesus won't be your Saviour. If you won't fear God, repent of your sins, deny yourself, lose your life for Christ and the gospels sake, turning to Jesus Christ for Who Jesus really is, you won't be saved. Is that so hard to add to the equation in the explanation? Won't people find "accept Jesus as your Saviour," much easier to accept? Sure. But it won’t save them. And regardless, is that what Jesus our Saviour gave us as an example to do?
Rom 6:23 says "the gift of God is eternal life through Jesus Christ our Lord." Eternal life is a gift. So we get that gift by simply accepting it, right? It doesn't say, but we could listen to Peter, on the day of Pentecost, who said “Repent . . . and ye shall receive the gift of the Holy Spirit" (Ac 2:38). He said, "Repent and you get the gift," not "accept the gift and you get the gift." Eternal life is through Jesus Christ our Lord. “Through. Our. Lord." You get to that gift through Jesus Christ our Lord. That requires repentance which is wholesale turning with the mind, will, and emotion (sorrow) from your sins, self, stuff and people, in surrender to Jesus Christ our Lord. This is how Jesus taught sinners how to be saved in Matt 10:32-39; 16:24-26; Mk 8:34:38; 10:21-31; Lk 9:23-26, 57-62; 13:1-9, 23-30; 14:25-15:32; 17:32-33; 19:1-10, 12-27 for instance, so He could be their Saviour.
Read here for further treatment of repentance: Repentance is Not Just a Change of Mind and here for Lordship Salvation, which is the Only Salvation.