Direction of arrival (DoA) estimation for sound source localization is increasingly prevalent in modern devices. In this paper, we explore a polynomial extension to the multiple signal classification (MUSIC) algorithm, spatio-spectral polynomial (SSP)-MUSIC, and evaluate its performance when using speech sound sources. In addition, we also propose three essential enhancements for SSP-MUSIC to work with noisy reverberant audio data. This paper includes an analysis of SSP-MUSIC using speech signals in a simulated room for different noise and reverberation conditions and the first task of the LOCATA challenge. We show that SSP-MUSIC is more robust to noise and reverberation compared to independent frequency bin (IFB) approaches and improvements can be seen for single sound source localization at signal-to-noise ratios (SNRs) below 5 dB and reverberation times (T60s) larger than 0.7 s.