Why A Sign of Jonah? (Matthew 12:22-37)

It seems that the leaders of Israel are coming around to understanding the significance of Christ’s ministry.  They simply want a sign, but Christ is upset with them for requesting a sign.  Jesus gives them a sign, but he gives them a sign of the AWOL prophet in the Old Testament.  Does this mean that Jesus is going to go AWOL or is there something deeper that Christ desires to communicate?