This paper presents a robust method for two-dimensional (2D) impulsive acoustic source localization in a room environment using low sampling rates. The proposed method finds the time delay from the room impulse response (RIR) which makes it robust against room reverberations. We consider the RIR as a sparse phenomenon and apply a recently proposed sparse signal reconstruction technique called orthogonal clustering (OC) for its estimation from the sub-sampled received signal. The arrival time of the direct path signal at a pair of microphones is identified from the estimated RIR, and their difference yields the desired time delay estimate (TDE). Low sampling rates reduces the hardware and computational complexity and decreases the communication between the microphones and the centralized location. Simulation and experimental results of an actual hardware setup are presented to demonstrate the performance of the proposed technique.