Low-frequency sound attenuation is often pursued using Helmholtz resonators (HRs). The introduction of a compliant wall around the acoustic cavity results in a two degrees-of-freedom (2DOF) system capable of more broadband sound absorption. In this study, we report the amplitude-dependent dynamic response of a compliant-walled HR and investigate the effectiveness of wall compliance to improve the absorption of sound in linear and nonlinear regimes. The acoustic-structure interactions between the conventional HR and the compliant wall result in non-intuitive responses when acted on by nonlinear amplitudes of excitation pressure. This paper formulates and studies a reduced order model to characterize the nonlinear dynamic response of the 2DOF HR with a compliant wall compared to that of a conventional rigid HR. Validated by experimental evidence, the modeling framework facilitates an investigation of strategies to achieve broadband sound attenuation, including by selection of wall material, wall thickness, geometry of the HR, and other parameters readily tuned by system design. The results open up new avenues for the development of efficient acoustic resonators exploiting the deflection of a compliant wall for suppression of extreme noise amplitudes.