Online social networks, such as Twitter and Facebook, form a substrate for the spread of information with unprecedented capabilities. In these new channels of communication, users can exchange information in an almost instantaneous and not mediated way, leaving fingerprints of their social behavior in the online realm. One of the main characteristic features of these communications networks is that users prefer to interact with others ideologically similar to them, creating echo chambers. These echo chambers are believed to facilitate misinformation spreading and contribute to radicalize the political discourse. In this work, we gauge the effects of polarization over the spread of information by quantifying the political leaning of users in the description of the associated echo chambers. Mining 12 million Twitter messages, a social network of users interchanging opinions related to the impeachment of the former Brazilian President Dilma Rousseff was reconstructed. A continuous political leaning parameter was inferred from a hand-tagged analysis of the hashtags adopted by users, which were assigned with anti-impeachment, pro-impeachment, or neutral leanings. This parameter, independent of the network's structure, allows to quantify the presence of echo chambers in the strongly connected component of the network. As a result, two well-separated communities of similar sizes with opposite views of the impeachment process was obtained. Taking into account the full temporal evolution of the social interactions, we use simple spreading models to characterize the efficiency of single users to spread information. We show that the capability of users in propagating the content they produce strongly depends on their political orientation: users expressing pro-impeachment leanings are capable to transmit information throughout the network, on average, to a larger audience than users expressing anti-impeachment leanings. Furthermore, we discover that users with larger spreading capacity are able to escape their echo chambers by reaching individuals with more diverse leanings. Our method can be exploited to identify the presence of echo chambers and their effects across different contexts and shed light upon the mechanisms allowing to break echo chambers. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001.