I should add to this: this is assuming the damage was reasonably necessary to the search. SCOTUS has said that extensive or unnecessary damage will violate the fourth amendment, even if the search was lawful and the fruits of the search not subject to supression. So if they smashed up everything in your house looking for one joint you would probably be able to sue them.
This is very similar to a situation I encountered while in college.
I was on my way to a Grateful Dead concert and was stopped by a State Trooper (as were a great many folks in the vicinity of the venue). The Trooper asked me if I had any drugs in the car, to which I responded “No” (I knew there would be plenty available at the venue - no need to carry my own). He then asked if he could search my vehicle. I hesitated and he said, “Listen, if you don’t give me permission I’m going to call for the canine unit and we’ll have to tear your car apart. Why don’t you just make this easier and let me search the car.” I was sufficiently intimidated to let him search and he didn’t find anything - not so much as a lighter.
I used to work for one of the national laboratories years ago, and you better believe they searched vehicles as they exited the premises. My own car was searched several times.
Ed
About the sign: I don’t know of any cases where somebody has tried that, so it’s hard to say. I’ll bet the goverment would argue what you did, i.e. park there, was more important to your consenting than what you said. And as you say, it wouldn’t get past the other leg of the argument.