Well, I'll tell you what. I hope it never happens but if the police ever bust down my door like has happened in some states (Florida...I'm giving you a HARD look!), they would probably get shot. I am armed, I keep one in every room within reach, and I generally am carrying as well. We have a castle law in this state and I'm not afraid to put one in somebodies head if they break in my house. I consider cops breaking down my door....warrant or not....to be breaking and entering.
They have every right to enter,because under the law,they can interrogate any suspect on basis of their "grounds".I think that if there is some kind of complaint coming from within the home, they have the right to enter. Other than that, I'm really not sure. You might need to ask a professional in that field.
I had the police show up here at my house about a year ago. I freaked out when they pulled in the driveway, because I couldn't imagine why they were here. I met them outside, in the walkway, and asked what they wanted. I have no issues with the police, but I figured it would be easier to meet them out there, since I've always got pets trying to get out and strays trying to get in the house when the doors are opened. It turned out that (no surprise to me) someone who used to live here had gone AWOL from military service, and they were looking to see if he was here, or still lived here. They didn't ask to come in and look around, once I told them he was no relation to me, and I've been living here for years, and had never met the family.