The sick people who were healed needed no convincing: Jesus had God’s authority and must be from God, possibly the Messiah (John 9:30-33).  But the religious leaders did not want any Messiah from God: they believed it was their right to have power over the people. So they were trying to find any reason to accuse Him in order to get rid of Him (Luke 22:2).  But, at the same time, they were also intrigued, wondering how He did His miracles, as though He was some kind of illusionist or fairground curiosity.  King Herod had the same mindset (Luke 23:8).
 
They asked Jesus for a sign.  But they did not want to see where any sign would point - they did not want to conclude that Jesus was God in a human body.  So the Master refused their request.  Instead He categorised their obsession with worldly power as wickedness, and their self-worship as adultery against God.  However religious a person might be, if they refuse to worship Jesus, they cannot love God with all their heart (Deuteronomy 6:5); they love other things or people more.  Spiritual adultery starts by falling away from our 'first love' who should be Christ (Revelation 2:4-5).
 
Jesus said that there was no need for any more signs as many eye witnesses had already seen His miracles without understanding what they meant.  But He pointed back to Jonah's experience inside the great fish (Jonah 1:17).  Not only did Jesus validate the historicity of Jonah's ordeal at sea, but the Lord used the prophet's three days of 'burial' as a sign that He would be buried and rise again on the third day.  
 
Many of us only see signs in retrospect.  We find it difficult to make a connection with something we have not experienced; however, afterwards we can see, if we do not refuse to believe (John 2:22).  The signs Jesus wants us to follow are not usually mysterious or inner feelings, they are obvious and well documented in the Scriptures.  Refusal to take Scripture seriously is another sign of a wicked and adulterous heart.  Why?  Because, in the Bible, God has already given enough information to understand who He is and how to worship Him.  Anyway, why should God give you another sign if you have refused to follow the signs you have already received?