Twitter as a new form of social media potentially contains useful information that opens new opportunities for content analysis on tweets. This paper examines the predictive power of Twitter regarding the US presidential election of 2012. For this study, we analyzed 32 million tweets regarding the US presidential election by employing a combination of machine learning techniques. We devised an advanced classifier for sentiment analysis in order to increase the accuracy of Twitter content analysis. We carried out our analysis by comparing Twitter results with traditional opinion polls. In addition, we used the Latent Dirichlet Allocation model to extract the underlying topical structure from the selected tweets. Our results show that we can determine the popularity of candidates by running sentiment analysis. We can also uncover candidates popularities in the US states by running the sentiment analysis algorithm on geo-tagged tweets. To the best of our knowledge, no previous work in the field has presented a systematic analysis of a considerable number of tweets employing a combination of analysis techniques by which we conducted this study. Thus, our results aptly suggest that Twitter as a well-known social medium is a valid source in predicting future events such as elections. This implies that understanding public opinions and trends via social media in turn allows us to propose a cost- and time-effective way not only for spreading and sharing information, but also for predicting future events.