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Unlike traditional search engines that present ranked lists of webpages, generative search engines rely solely on in-line citations as the key gateway to original real-world webpages, making it crucial to examine whether LLM-generated citations have biases—particularly for politically sensitive queries. To investigate this, we first construct AllSides-2024, a new dataset comprising the latest real-world news articles (Jan. 2024 - Dec. 2024) labeled with left- or right-leaning stances. Through systematic evaluations, we find that LLMs exhibit a consistent tendency to cite left-leaning sources at notably higher rates compared to traditional retrieval systems (e.g., BM25 and dense retrievers). Controlled experiments further reveal that this bias arises from a preference for media outlets identified as left-leaning, rather than for left-oriented content itself. Meanwhile, our findings show that while LLMs struggle to infer political bias from news content alone, they can almost perfectly recognize the political orientation of media outlets based on their names. These insights highlight the risk that, in the era of generative search engines, information exposure may be disproportionately shaped by specific media outlets, potentially shaping public perception and decision-making.