I suspect Jesus sighed as the HolySpirit was grieved by the foolish, blindness of the question. Jesus asks why they want a sign. do they want to believe? If they did the signs He gave in His healings, miracles and exorcisms were more than sufficient.
He says in this place there will be no sign given to the Jews of that generation (of that persuasion). They were all doomed for rejecting the signs that He performed.
In another place He shares that the sign of the prophet Jonah who was 3 days and nights in the belly of the great fish before being spewed out is the sign of all signs.