1. You attacker is not behind ANY kind of cover. Not even a couch, appliance or drywall.
2. Your attacker is 12' or closer.
3. Your attacker is lightly clothed, or even better, naked.
4. Your attacker is the same size or smaller as the average male (about 19" shoulder to shoulder and about 9" front to back)
5. Your attacker is facing you with his hands out to the sides providing an unobstructed center mass shot.
If any of those conditions change, 12ga #6 birdshot loses a lot of effectiveness. You've made a choice to limit the potential liability by limiting the effectiveness of the firearm to a fairly narrow range so you don't have to worry as much about shoot or don't shoot decisions in a high-stress scenario. That is certainly one way to approach the problem. However, I would submit that making the firearm more effective, getting training, and utilizing a little prior planning to identify safe backgrounds and no-shoot backgrounds gives you more options and ultimately makes your family safer by being more likely to stop the threat that made you decide that firing a gun inside the house was less dangerous than not firing to begin with.