The steered response power (SRP) approach to acoustic source localization computes a map of the acoustic scene from the frequency-weighted output power of a beamformer steered towards a set of candidate locations. Equivalently, SRP may be expressed in terms of time-domain generalized cross-correlations (GCCs) at lags equal to the candidate locations' time-differences of arrival (TDOAs). Due to the dense grid of candidate locations, each of which requires inverse Fourier transform (IFT) evaluations, conventional SRP exhibits a high computational complexity. In this paper, we propose a low-complexity SRP approach based on Nyquist-Shannon sampling. Noting that on the one hand the range of possible TDOAs is physically bounded, while on the other hand the GCCs are bandlimited, we critically sample the GCCs around their TDOA interval and approximate the SRP map by interpolation. In usual setups, the number of sample points can be orders of magnitude less than the number of candidate locations and frequency bins, yielding a significant reduction of IFT computations at a limited interpolation cost. Simulations comparing the proposed approximation with conventional SRP indicate low approximation errors and equal localization performance. MATLAB and Python implementations are available online.