I teach, and practice, shooting until one's target is gone. There are several ways of doing this with a rifle in a training environment. Please do not rehearse preparing to defend your family by wasting a good sight picture! If a deer hit through the vitals with a 7 mag can run 50 yards before he knows that he is dead, a felon hit through the vitals with a .223 can murder your family before he realizes that you have killed him.
When it comes to defense, if you wind up ever having to do it, you will find that it happens in a nanosecond. From the moment when your mind says 'Start shooting' and you draw or you drop that hammer, the world goes into slow motion. Lots of things go through your mind; jump for cover? Run this guy over? Shoot him again? Run for your life? Get in front of innocents and guard them- I will tell you, your brain is going to run this program very fast. When the hits come (Hoping they are not on you) the situation will change. You are both now all in; cards are now on the table, and the hand will play out. In the 2 instances where I have been in this situation, one was a one shot stop. I put one right next to the person's head, thru glass. His weapon hit the ground instantly. It saved his life, by reacting so quickly. I never heard him shouting 'Stop, I give up', whatever he said. All I knew was what I saw and took in and processed it in an instant. The trigger was already heavy under my finger, and the second shot was pointed center mass. I am really glad that he did drop the gun, and I am glad that I correctly held off on sending the second round out.
The one mistake was the warning shot. I will say; DO NOT EVER, under any circumstances give a 'warning shot'. I will explain:
It's a Thursday night, about 1am. My truck alarm goes off for about 5 seconds; really quickly stopped. I hustled out of bed, and knew this was not a sideswipe from a drunk driver or similar situation. I came out my front door, and saw a Camaro stopped crossways in front of my truck. The passenger door was open about halfway, toward the curb. There was a person in my truck, working the column. As I announced myself, the person in the passenger seat fired a warning shot directly into the ground under my feet. He aimed this, to be certain. Dead center in front of me, about 3 feet under me (I lived on a raised lot about 5 ft high, with a high sloped yard.) The person jacking the truck brandished a weapon immediately as he was clearing around my truck heading for the car. I took the warning shot 100% seriously, and I responded. It's not what you want to have to do. But it happens.
For me, the warning shot from 2 years prior and the training to get myself away from that left me in a position that eliminated a good deal of wasted time. When not wasting time, you can work. When faced with a person hedging their bets and using a warning shot to buy time, it gave me time to weigh options when I was NOT 'working' or 'wasting time'. I had a half second to evaluate things; and react.
I will say, the passenger in the car got the jump on me. I will say with confidence, your good-natured, law abiding mentality WILL allow most people to get the jump on you. I sure did. Even with a lot of training. "Who and why would someone actually SHOOT ME???!!!" Eyep; that's what your brain says.

Anyway, the thing is when I was put into this second situation, there was no stopping at one shot, or 2 shots. I was committed to stopping the threat on me, and that was with more than 1 armed perpetrator. All said and done, the training I did performed one very good task. It engrained into me to A. Stop the threat. And B. It stopped me before wasting ammunition, so I was still viable in protecting myself from any other threats.
The driver of the car never moved an inch; he dove down in his seat, tried to get real small, and would not move for anything until the police showed up. He was content to go with them.
Had he gotten agressive, I was able to conserve some ammo so that I would have at least had a chance to engage and try to protect myself.
And, yet I failed a critical task yet again: I STILL was standing there, thinking the whole time: "What; why would somebody actually try to shoot ME?" And I seriously hesitated, without taking cover, and had this driver been a different sort of person, there would have been an even bigger mess on my hands. Had he been in there with a shotgun with buckshot? I'll say it; I hesitated way too long in the open, even though I more than doubletapped 2 times in 10 seconds.
A second is about 3 times as long as it takes for a bullet to catch up to you.
I agree with Matt; if you are ever in a situation where you must shoot? Do it like a Cicago voter. Shoot early, shoot often.