Examining the alignment of large language models (LLMs) has become increasingly important, e.g., when LLMs fail to operate as intended. This study examines the alignment of LLMs with human values for the domain of politics. Prior research has shown that LLM-generated outputs can include political leanings and mimic the stances of political parties on various issues. However, the extent and conditions under which LLMs deviate from empirical positions are insufficiently examined. To address this gap, we analyze the factors that contribute to LLMs' deviations from empirical positions on political issues, aiming to quantify these deviations and identify the conditions that cause them. Drawing on findings from cognitive science about representativeness heuristics, i.e., situations where humans lean on representative attributes of a target group in a way that leads to exaggerated beliefs, we scrutinize LLM responses through this heuristics' lens. We conduct experiments to determine how LLMs inflate predictions about political parties, which results in stereotyping. We find that while LLMs can mimic certain political parties' positions, they often exaggerate these positions more than human survey respondents do. Also, LLMs tend to overemphasize representativeness more than humans. This study highlights the susceptibility of LLMs to representativeness heuristics, suggesting a potential vulnerability of LLMs that facilitates political stereotyping. We also test prompt-based mitigation strategies, finding that strategies that can mitigate representative heuristics in humans are also effective in reducing the influence of representativeness on LLM-generated responses.