Using critical discourse analysis (CDA), we explored how educational leaders and policymakers in Mexico, Peru, Chile, and Argentina address complex issues while responding to -- and in fact, developing -- broader understandings (discourses) on the role of higher education in Latin America. Fairclough's (1993) theory of discourse underscores that language is a social practice, socially and historically situated, and encompassing social identities, relations, and systems of knowledge and beliefs. Therefore, discourses, which are represented by all kinds of texts, exercise power because they can produce, reproduce, and transform social structures, including education policy. This study uncovers the nuances of the tensions that globalized discourses such as neoliberalism in particular face when met with national and local needs in Latin American higher education. These tensions need to be addressed in order to design policies that could effectively close the equity gap in the region amidst massification and the uncontrolled proliferation of private universities in many countries, offering access to underserved students to higher education but of questionable quality. This study suggests research like this is important in order to understand how discourses that are deemed global play out at national and local levels and possibly, to uncover alternatives to the status quo.