I'm not really concerned what what lawyers (*hawk spit*) have written or defined.
Rights in the constitution come from a higher authority than them. Popo can come back with a warrant unless there's a gun fight runnin, I don't care if they are looking for Osama Bin Ladin. Not that I have any fantasies about how that would go down, but I have my principals and I'll stick to them. 
I'm not trying to get into a spitting match with you, DR, but....
I guess I did mis-speak a little - I blame the lawyers, but ultimately the Supreme Court has interpreted what phrases in the Constitution mean. It doesn't really matter what you think is reasonable, but what the law (as jacked up as it may be) has come to determine what reasonable means.
Standing on principal is all well and good, but you've gotta choose your battles. Having a battle to the death over allowing a cop enter your home doesn't get you anything but dead. Telling them clearly that they don't have your permission to enter, but not forcefully resisting when the insist will allow you to fight another day in court (and not from jail) and then fight the illegal entry as a means to try and change the jacked up interpretation of "reasonable."
I'm not saying that you'd have a fight to the death to keep the police out - but if that's your position ... Well, good luck with that.
Bill