Jonah as a Parable
Matt 12:38-40 NIV The Sign of Jonah
38 Then some of the Pharisees and teachers of the law said to him, "Teacher, we want to see a sign from you.” 39 He answered, "A wicked and adulterous generation asks for a sign! But none will be given it except the sign of the prophet Jonah. 40 For as Jonah was three days and three nights in the belly of a huge fish, so the Son of Man will be three days and three nights in the heart of the earth.
Luke 11:29-30 HCSB
29 As the crowds were increasing, He began saying: "This generation is an evil generation. It demands a sign, but no sign will be given to it except the sign of Jonah. 30 For just as Jonah became a sign to the people of Nineveh, so also the Son of Man will be to this generation.
From Defending Inerrancy, Normal L. Geiser, William C. Roach, p.230-231 "For example, when Jesus affirmed that Jonah was in "the belly of the great fish," this statement is true, not simply because of the redemptive significance the story of Jonah has, but because it is literally and historically true [i.e., it corresponds to reality]." (Italics original.)
By calling attention to the verse in Matthew, the inerrantists indirectly refer to the parallel verse in Luke. According to Luke, Jesus did not mention Jonah being in the belly of a whale. Hence, instead of defending inerrancy, the authors inadvertently weaken their case and end up defending errancy. The two statements by Jesus are very different. The question of course is, which of the two is correct?
The statement may not be true if one accepts the testimony of Luke. Ignoring this significant problem for the moment, in the Matthew context, Jesus could be referring to either a true story, or a parable-prophecy of His forthcoming resurrection. It is not unreasonable to assume Jesus knew it was a parable, since He used many parables to teach about the kingdom of God.
Some level of support comes from  "The book of Jonah is considered by some to be a parable to convey a theological point about God's attitude towards Gentiles."
A plausible view is that Jonah was dead during his three days in the whale and, like Lazarus in John 11, his life was restored after he was disembarked onto dry land (2:10). But in ch. 2 he prays while inside the great fish. Acceptance of this as historical fact incurs a severe case of heartburn.
It is certain that Jesus was dead when "in the heart of the earth for three days and three nights," because the truth of the Resurrection demands this. But Jonah wasn't dead while in the whale, but alive and praying. Hence, if the story of Jonah is true, the comparison of Jonah with Jesus is not exact. But as a parable-prophecy of Jesus' impending resurrection, the analogy does not have to be exact.
Did the people of Nineveh know that Jonah had been in the belly of a whale for three days? Not according to the book of Jonah. He preached repentance to Nineveh after he left the whale. (Jonah 3) What "sign" then was Jesus referring to? As mentioned previously, from the context in Matthew, He was referring to the three days and nights in the whale, in spite of the fact that Nineveh was apparently not aware of Jonah's 72-hour voyage. Per Luke 11, the only sign for Nineveh was the appearance of Jonah voicing his warning of destruction in 40 days. (3:4)
The city of Tarshish is somewhere in the western Mediterranean; some think it was on the Atlantic side of ancient Spain. Jonah boarded his ship to Tarshish in Joppa, (present-day Jaffa) which is on the coast of Palestine about 35 miles from Jerusalem. The whale apparently carried him eastward from the ship back to the eastern shore of the Mediterranean in Palestine.
The city of Nineveh was located on the Tigris river, in present-day Iraq. From the closest point of eastern Mediterranean shoreline, Nineveh is about 370 miles from the Mediterranean Sea. Hence Jonah had to walk across the deserts of Israel, Syria, and Iraq to reach Nineveh. Assuming he could walk 25 miles a day (or night), this would be about a 15-day journey. Jonah could barely stand one day in the heat (4:8) much less 15 days. This is another miracle in the book of Jonah that few people take note of. However, as a parable, it is not important how he got there.
As an aside, pastor-author Chuck Swindoll is an ex-Marine, and was stationed with the 3rd Marine Division on Okinawa. In one of his sermons he said: "When the whale belched Jonah up on the beach at Nineveh, this was the first amphibious landing in recorded history."
 HCSB Study Bible, Holman Bible Publishers, 2010, p.1514