From scanning that paper, I'm guessing that talking about willpower as a limited resource causes those in that group to assume that willpower is not only limited but small and about to run out as well.

So for example, if one were to talk about sunlight as being a limited resource (which it is), it carries the implication that that limit is close enough to worry about.

People's attention is drawn to the idea that they will run out of willpower. The first time they start to experience depletion, they give up, because they assume they've run out.

It would be interesting to repeat the experiment, but tell the participants that in addition to the normal amount of willpower, they also have a secondary reserve which, with a little more effort, they can tap into to double or triple their performance.