Motivated by privacy and security concerns in online social networks, we study the role of social pressure in opinion games. These are games, important in economics and sociology, that model the formation of opinions in a social network. We enrich the definition of (noisy) best-response dynamics for opinion games by introducing the pressure, increasing with time, to reach an agreement.We prove that for clique social networks, the dynamics always converges to consensus (no matter the level of noise) if the social pressure is high enough. Moreover, we provide (tight) bounds on the speed of convergence; these bounds are polynomial in the number of players provided that the pressure grows sufficiently fast.We finally look beyond cliques: we characterize the graphs for which consensus is guaranteed, and make some considerations on the computational complexity of checking whether a graph satisfies such a condition.