Understanding the ability to measure and discriminate particle events at the lowest possible energy is an essential requirement in developing new experiments to search for weakly interacting massive particle (WIMP) dark matter. In this paper we detail an assessment of the potential sensitivity below 10 keV in the 1 m^3 DRIFT-II directionally sensitive, low pressure, negative ion time projection chamber (NITPC), based on event-by-event track reconstruction and calorimetry in the multiwire proportional chamber (MWPC) readout. By application of a digital smoothing polynomial it is shown that the detector is sensitive to sulfur and carbon recoils down to 2.9 and 1.9 keV respectively, and 1.2 keV for electron induced events. The energy sensitivity is demonstrated through the 5.9 keV gamma spectrum of 55Fe, where the energy resolution is sufficient to identify the escape peak. The effect a lower energy sensitivity on the WIMP exclusion limit is demonstrated. In addition to recoil direction reconstruction for WIMP searches this sensitivity suggests new prospects for applications also in KK axion searches.