I have not used it in a N.E.W. game yet (circumstances conspired against us last week and we had to cancel our session) but I did use this mechanic for a couple things the week before in our D&D Next game. Here's how I used it.
1- Pollution / Taint
The PCs found two magical teeth that had been extracted from the mouth of a demon. These teeth have powers but when they are used they cause a slow pollution of the boy and soul. Each PC started out at 6 and whenever they use a power of the tooth they roll.
2. Hide & Seek
The party was searching through the ruins of a city where a powerful demon had made a nest. This demon was attuned to the area and could feel intrusions. I used a 3-dice countdown, checked every 30 minutes, to determine when the demon located the PCs. This pool was enlarged by Hide checks and additional countdown rolls were made when they did certain things (such as using a divine power).
I have not made extensive enough use yet to know if this is going to be a good balanced way of tracking these things but I love the simplicity of the rule. Before reading this in your N.E.W. book I would have used different mechanics for each of the above, of varying levels of complexity. The countdown mechanic proves a nice, standard, simple way to resolve these things.
The only thing I didn't like, is that, in some cases, taint for example, reversing the order would make more sense. Ideally I'd like the PCs to have a taint score of 0 and work upwards, but the countdown works opposite that. It doesn't really matter, just made it slightly harder to explain (and that really only mattered because this was how I introduced the mechanic to them).