The reason Tiger is so unflinching from this distance is because he’s not afraid to release the putterhead. Most players tend to miss their putts to the right under pressure (see Tom Watson at the Open Championship) because their grip gets tighter and the putterface stays open through impact. This negatively impacts both the speed and direction of the putt – if you recall, Watson’s par putt on the final hole of the Open Championship didn’t even touch the hole.
Tiger works on his release all of the time in practice, and you can, too. Hit several putts on the practice green from six to 10 feet, and as you swing the putterhead through impact, feel as if the knuckle on your left index finger gets to the target faster than the pinkie on the same hand. This will encourage the face to close through impact. As you practice, keep your grip pressure constant through the stroke; so, if you’re pressure is a five (on a scale from five to 10), hold it at five until the ball is well on its way.