I agree with Mr. Moore from a conventional wisdom standpoint. However, my experience has been otherwise. I have a Remington Model 700 chambered in .222 Remington (similar ballistics to a .223) that I used to shoot untold numbers of prairie dogs with in my teen years in the Texas Panhandle. I started hunting whitetails in high school and used the .222; partly out of "ignorance" I suppose and partly because of the effect it had on prairie dogs out past 200 yards and on steel plates. I know a dog is not a deer and if I was starting deer hunting today, I would probably think a .222 is not enough gun. But here is my experience:
I have shot at and killed four deer and killed all four with the first shot of a Sierra 50 grain spitzer at 3200 ft/sec. Two were head shots at 60-80 yards which dropped them like a sack of bricks. The third was a neck shot which also collapsed the deer immediately. My most recent was the classic just-behind-the-shoulder shot at 125 yards. The deer bucked and ran 20 yards and then collapsed dead. I recovered the bullet. It had passed through the chest cavity collapsing both lungs and stuck in the hide on the far side. The spitzer had expanded to form a mushroom between 3/8 and1/2 inch in diameter and had retained its structural integrity.
A fifth deer was killed with this same gun and load by my father-in-law while I sat behind him and observed. He hit the deer high and too far back thus missing the vitals. The distance was about 40 yards. However, the bullet did enough damage that the spinal cord was affected and the deer didn't move an inch. He finished the deer quickly with a second shot to the head after approaching the deer.
In addition to these deer that I saw shot, my brother reports that he cleanly killed the only two deer that he shot with a mini-14 .223 he owned several years ago.
I think the critical factor with any kind of stopping situation is shot placement. For example, I am much more confident of a humane kill from my Model 700 .222 which puts a bullet where I want it to than I would be with a shoulder cannon that I can't shoot as well (whether due to poorer accuracy in the gun or flinch or whatever). On the other hand, there are certainly plenty of conventional deer calibers that are light recoiling and harder hitting than a .222 or .223. I wouldn't necessarily recommend the .223 or .222 for deer either. But, in my experience, a .222 in a gun that I can shoot well has done very well on whitetails.