Generally speaking, they will have to convince a Judge that they have sufficient evidence to obtain a warrant. It HAS TO BE SIGNED BY A JUDGE. It isn't like they have a bunch of them in a drawer somewhere that they can just go back and get. If they have nothing more than the fact that you refused to let them search, they may as well leave. No judge wants to be overturned, or burned issuing a warrant based upon insufficient, or constitutionally deficient information.
Now in reality most detectives have a judge who will issue a warrant based upon the officer swearing that they have probable cause, but god help that cop if the warrant gets tossed for lack of probable cause.
In short, it aint just that easy for a cop to get a warrant. They would love us to believe that they can just go get one, but they can't. If they show up at your door, and ask if they can come in, or if you have a problem with them "looking around" they haven't got shit. If they did, they'd show up WITH a warrant.
If cops come to your door, go out and close the door behind you. Answer thier questions, be polite, but refuse to let them enter the premises without a warrant. DO NOT let them intimidate you into believing that they have to make a "required" search of the premises, or that they will "just come back with one". You do not owe them an explanation. just say no, and goodnight officer. Trust me, thats the last you'll see of them.
A suggestion, put a video camera (real or fake) outside and aimed at your door. If they start intimidation tactics, or try to bully thier way in, just point to the camera and say "Smile, we are being recorded, and I have this whole thing on tape". I guarantee that they will change thier tune!!!
