For once the Pharisees have a legitimate concern. If the Romans take notice of these kinds of goings-on, then things could get ugly.
In general, Romans had a couple of ways to deal with insurrections or potential insurections: Kill everyone before trouble started, or kill everyone after trouble started. Since the Judeans had been problems since nearly day one, what with their crazy idea of just one god and refusal to accept the divinity of the Roman Emperor, then the chances were pretty good that they would go for plan A. Which is what the Pharisees were worried about (as it turns out, they actually went for plan B during the uprising in AD 70, destroying Jerusalem and wiping out their problem once and for all).
While the Roman governor generally looked the other way on most things as long as tax collections kept up, a mob proclaiming someone as king was not on that list. So the Pharisees' warning was probably sincere and represented a real danger. "Rabbi!" they called. "Ix-nay on the osanna-hay! Omans-ray!" This was ineffective, not the least because speaking pig Latin is probably not a way to keep Romans from understanding you.
But the real reason was what Jesus told them. If the crowd quieted, the stones themselves would cry out. See, this was not just a crowd acclaiming a leader or proclaiming some kind of earthly ruler. The people were responding to the very presence of God in the person of Jesus. The only possible response was praise. The hosannas and palms and cheering all came about as a kind of spontaneous combustion, and Jesus tells the Pharisees that if the people don't respond then the stones of the road will.
Now, should that have happened and the stones began singing the praise of the Lord of creation, then what would have happened after Jesus had ridden past? What would the stones have done then? Probably stayed stones; Jesus doesn't seem to be suggesting that they would become his followers. The ideal way creation responds to its creator is through the praise from that part of creation made in the creator's image. If that part doesn't do its job, well, then other parts can pick up some of the slack but not all of it.
I see this as instructive for us as the church today. We have any number of complaints with various social structures and the way they handle some of their tasks, and we have them regardless of which side of the political divide we fall. We may say that social workers, many of whom are dedicated people trying to help folks in need, aren't getting everything done that they should be doing. Those same social workers, staring at overwhelming case loads and problems their system was never designed to handle, might agree.
Well, what should we expect? Governmental agencies are stones shouting praise -- they can do it when the ones who are supposed to be helping don't measure up, but they'll never do it from the same place Jesus' followers could. Agencies and bureaus and departments help people in need because they're in need. Christians help people in need because they're people, children of God just like us.
Jesus offered himself on the cross for you and for me, for everyone, so that we might have the relationship with God we were designed to have and desire. But having reconciled us, he then called us to service with him. Helping the poor and hungry, aiding the sick -- all of this -- it's our job, church.
And it's time we stopped leaving it to the rocks.