Jesus' Public Proclamation that He is the Messiah

Getting back to our story, Jesus was traveling with a crowd of Galilean Jews south to Jerusalem to celebrate the Passover. They had just passed through Jericho, where a blind man has called Jesus the "son of David," most likely suggesting that he considered Jesus to be the Messiah, who was to be a descendant of King David. Jesus seems to accept this designation, for the first time publicly acknowledging that he also considers himself to be the Messiah.

It is about another 15 miles to Jerusalem, or roughly an 8 hour hike. When they get close to the city, Jesus sends someone to get a donkey, which he then sits on to ride into Jerusalem. We are told in the New Testament accounts that this is to fulfill a prophecy in Zechariah 9:9. 

" Rejoice greatly, O daughter of Zion!
Shout aloud, O daughter of Jerusalem!
Lo, your king comes to you;
triumphant and victorious is he,
humble and riding on an ass,
on a colt the foal of an ass."

I suspect that most Jews would have been familiar with that prophecy and would have understood that Jesus was now making a public proclamation that he was the Messiah, the rightful king of Israel. The crowd that is with him threw down their garments and leafy branches on the road and cried out, “Hosanna! Blessed is he who comes in the name of the Lord! Blessed is the kingdom of our father David that is coming! Hosanna in the highest!” 

Any Jews watching from Jerusalem would realize the serious Messianic implication of Jesus triumphal entry. But what about the Romans? I suspect that a man riding a donkey into the city wouldn't have meant much to them. And there was no show of military force. So if this triumphal entry had caught their attention, they might have just shrugged it off as some silly Jewish show of honor to one of their religious men. 

However, if the priests, the men in charge of the Temple and responsible for civic order in the city, saw Jesus' entry, I think they would have been very alarmed. Who was this man and why was he seemingly claiming to be the Messiah? And what were they to do about it?