My problem with this is: first, it seems like an incomplete telling of the story of Jonah (there is more to the story than Jonah disobeying God and getting swallowed by a big fish for 3 days and then getting spit back out after). Second, it seems like a complete confusion of law and gospel. Third, it misses the point as to what the entire story of Jonah was about, and even why Jonah was swallowed by a big fish.
Jonah is an interesting book in the Bible, and it is an incredible story that can be hard to accept with human reason, and requires the reader to accept it because it is in the Bible, and because Jesus acknowledged it as real historical fact himself (Matthew 12:38-42, Luke 11:29-36). It is an incredible story about one of the prophets of the Old Testament (Jonah), who was sent on a mission by God to warn the people of the large city of Nineveh that their destruction is at hand unless they repent (turn away from) their sins and evil ways. Something akin to being told in the modern day to go to Las Vegas and tell the people there that they have to turn from their sinful ways and repent, or else God will destroy them.
Of course, Jonah does what any normal, rational person would do in the event of being told to do something so insane -- he runs from it. God punishes him with raising a storm, and eventually having him swallowed by a big fish (the Bible doesn't state it was a whale and it is best to take it as a literal fish, not inject human reason into the story and claim it is a whale, like God somehow can't make a fish big enough to swallow a man). Three days later, after he repents of his willful disobedience toward God (something that a prophet should have known better than doing int he first place), he is spit out from the fish, and goes to Nineveh -- where he proceeds to do as God told him to do -- tells the people of their impending doom unless they repent.
Surprisingly, rather than being laughed out of town, or executed for his insolence, the people believed what Jonah said, and repented of their sins -- thus they avoided the destruction that awaited them, God forgave the people of Nineveh, just as he had forgiven Jonah when he repented of (turned away from) his sin.
Which brings us to the crux of the matter -- was the point of the book of Jonah to show us that we must do what God says or else He will punish us? Or was the purpose for this story to show us another example of God's ceaseless mercy and grace? Is it a story about following the rules (Law), or was it a story about forgiveness (Gospel)? I will make the claim that it is a story about forgiveness. It is how God spared Jonah & Ninevah from their respective dooms when they repented of their sins. It isn't a story about how we should do what God wants for us or else we'll be punished.
The song has an obvious confusion between law and gospel -- and the writer should review Galatians 3 for reference as to what the distinction should be, and what place the Law really has.
For all who rely on works of the law are under a curse; for it is written, “Cursed be everyone who does not abide by all things written in the Book of the Law, and do them.” Now it is evident that no one is justified before God by the law, for “The righteous shall live by faith.” But the law is not of faith, rather “The one who does them shall live by them.” Gal. 3:10-12The Law shows us how much we fail to live up to it, and just how much we need God's forgiveness (given to us through Jesus' suffering, death, and resurrection). Making the story be purely reduced to "follow God's law or else!" strips the refreshing story of forgiveness within the passage. So, why is this story in the Bible? Well, basically, because it is a footnote in Christ's life. He referenced the book, specifically the Sign of Jonah, and used it as the only sign he would give, that just as Jonah spent three days and nights in the belly of the fish, so too will Christ spend three days and nights in the belly of the earth. It is a sign that points directly to the cross, pointed out by none other than Christ himself.
So, the entire point of the Book of Jonah could be summarized as being a marker that points directly to Christ's work -- his death and resurrection, the very act that triumphed over death and sin, and promises true salvation from both to those that believe. Hardly the point that had been derived into the lyrics of that song.