This is not the first time that Jesus had been asked for a "sign from heaven" (cf. Matt. 12:38). This is the only time recorded in the Scriptures, however, that the Pharisees and Sadducees worked together in opposition to Jesus (cf. Matt. 16:1). Of course, this fact is not surprising due to their extreme differences and animosity toward each other. But, they manage to work together on this occasion against a common enemy--Jesus!
Up to this point in Jesus' ministry, they have rejected His miracles and blasphemed the power of the Holy Spirit by stating that His power was of Beelzebub (cf. Matt. 12:22-32). They specifically ask for a sign "from heaven." Technically, since Jesus came down from heaven and all of His miracles were made possible via power from above, every sign of Jesus was "from heaven." But, what these religious leaders desired was a miracle that was worked in the sky and not on the ground (e.g., the sun standing still in Josh. 10, manna coming down from heaven in Exo. 16, lightning and trumpet sounds in I Sam. 12, thunder and rain in I Kings 18, fire from heaven in II Kings 1, etc.)! It would seem that they want to test the limits of Jesus' power and hopefully be able to conclude that there are certain kinds of miracles that He can't perform.
Jesus sighed deeply in His spirit. He was grieved at their hard-heartedness. Certainly He knows that if He performed a miracle of this category (i.e., "from heaven"), they still would not believe in Him because He had already done so many other miracles that clearly established who He was (cf. Matt. 16:16,17).
Matthew offers some additional details in His account of this narrative. Jesus responded to their request aggressively - "When it is evening you say, 'It will be fair weather, for the sky is red'; and in the morning, 'It will be foul weather today, for the sky is red and threatening.' Hypocrites! You know how to discern the face of the sky, but you cannot discern the signs of the times" (Matt. 16:2,3). Our Lord rebuked them after noting their correct insights into meteorology. His point was that although they understood the weather because they observed the signs, they had failed to understand His signs (i.e., miracles), though they were as plain as the color of the sky at sunrise or sunset. Jesus undoubtedly felt that it was useless to give new signs to those who were blind to the signs already existing!
Jesus continued in Matthew 16:4 - "A wicked and adulterous generation seeks after a sign, and no sign shall be given to it except the sign of the prophet Jonah" (cf. 12:39-41). The statement that "no sign" would be given didn't mean that Jesus wouldn't perform any more miracles; it simply meant that He wasn't going to grant their request for a sign "from heaven." However, Jesus did mention one exception to this rule--"the sign of the prophet Jonah." This is a veiled reference to Jesus' death, burial, and resurrection. Jonah was shown to be a true prophet of God, and Ninevah received him as such because he was rescued from the fish's belly (cf. Luke 11:30). In a similar manner, Jesus would be declared to be the Son of God via His resurrection from the dead (Rom. 1:4). As Jonah came forth alive after three days in a fish, so also would Jesus come forth alive after three days in a tomb. This would be the great sign Jesus would provide for His skeptics--and He did just that!