Social media platforms play a pivotal role in shaping public opinion and amplifying political discourse, particularly during elections. However, the same dynamics that foster democratic engagement can also exacerbate polarization. To better understand these challenges, here, we investigate the ideological positioning of tweets related to the 2024 U.S. Presidential Election. To this end, we analyze 1,235 tweets from key political figures and 63,322 replies, and classify ideological stances into Pro-Democrat, Anti-Republican, Pro-Republican, Anti-Democrat, and Neutral categories. Using a classification pipeline involving three large language models (LLMs)-GPT-4o, Gemini-Pro, and Claude-Opus-and validated by human annotators, we explore how ideological alignment varies between candidates and constituents. We find that Republican candidates author significantly more tweets in criticism of the Democratic party and its candidates than vice versa, but this relationship does not hold for replies to candidate tweets. Furthermore, we highlight shifts in public discourse observed during key political events. By shedding light on the ideological dynamics of online political interactions, these results provide insights for policymakers and platforms seeking to address polarization and foster healthier political dialogue.