Implicit content, such as implicatures and presuppositions, is a key feature of political discourse, allowing speakers to convey meaning indirectly and influence audience interpretation. While Large Language Models (LLMs) have demonstrated impressive capabilities in natural language understanding, their ability to process implicit meaning in real-world contexts remains an open question. This study investigates whether state-of-the-art LLMs can detect and classify implicit content in Italian political speech. Using a subset of the IMPAQTS corpus we assess nine multilingual models, both open-weight and proprietary. The study comprises two tasks: a binary detection task, where models determine whether a given sentence contains implicit content, and a binary classification task, in which models identify whether the implicit content is conveyed through implicature or presupposition. To enhance model performance, we employ six different prompting techniques. Results reveal that while some proprietary models exhibit moderate success in detecting implicit content, none surpass chance-level performance in classification. Open-weight models consistently underperform, with accuracy scores hovering near random guessing. Among prompting strategies, more structured techniques achieve marginal improvements in detection but fail to enhance classification accuracy. These findings highlight the persistent challenges LLMs face in pragmatic reasoning, defining implicit content detection and classification as unresolved tasks in NLP.