I'm thinking of my buddy back in Missouri -- not wealthy; not a lobbyist, PR professional, or any kind of professional -- who told me (more or less):
"It's unfair. It's the one tax you can't avoid. No matter what you do, you can't opt out. It's like you don't even own your own property. The government owns it. You never really own anything, as long as they can tax you just for existing on your own land."
That's the intuitive, everyman objection.
It is a sort of silly objection -- you can avoid property tax by having no property, in the same way that you can avoid income tax by having no income. I guess it is probably easier to evade income tax, than property tax, though.
edit: it seems obvious because of the thread topic, but property taxes are the most easily and intuitively justifiable tax. People with more property use more public services.