Numerous studies on political discourse claim that metaphors help politicians to construct coherent arguments to convince their voters. Yet, most of them, with a few notable exceptions, do not adhere to any theory of argumentation. In this paper, we integrate Discourse Dynamic Approach to Metaphor with Inference Anchoring Theory to enhance our understanding of the interaction of metaphors and arguments in dynamic discourse. Our data come from three pre-election debates: Two in Poland and one in the US. The focus is on the reform of the health service. We show how discourse participants co-construct metaphors and arguments in an attempt to achieve their illocutionary goals. Their interaction is curbed by a number of discursive forces identified in the data. We propose a classification of types of interaction between metaphors and arguments, which can be further used for developing tools for automatic or semi-automatic identification of these types in large corpora.