I think this tag comes from comparing him to those more skillful than him but who maybe when the skills aren't coming off (or the crowd are on their back) are more prone to be seen as 'hiding' or 'losing confidence'. Dempsey does keep plugging away even when things seem to be going wrong for him. Perhaps the most likely player that he gets compared to in this regard is Sigg.
Dempsey really doesn't press much and even Fulham fans used to call him lazy. Siggy and Holtby are substantially more hard-working throughout 90 min imo, though it is oftentimes headless chicken-running sort of effort. OTOH, you could say Dempsey 'preserves' his energy to keep looking for good chances up until the final second and his finishing seems to be very cool under pressure.