The phenomenon where a committed minority overturns established social norms, frequently witnessed in revolutions and elections, has drawn extensive attention as it powerfully showcases the profound influence of strong personal convictions. In order to unravel the underlying mechanisms of the crucial role of public opinion within the dynamic process where a committed minority can leverage negative public opinion to challenge the status and even overturn established norms when a critical threshold is reached, we investigated the effects of negative public opinion by integrating it into the well-established traditional naming game model. It was found that there exists an optimal range of negative public opinion influence, which facilitates the minority's ability to gain power and achieve social consensus. Notably, our results show that a smaller critical mass of committed individuals could trigger consensus behavior under this mechanism. The introduction of negative public influence into opinion propagation has yielded intriguing results, offering a new perspective on expanding consensus formation in opinion dynamics, particularly in diverse environments.