In recent years, significant concern has emerged regarding the potential threat that Large Language Models (LLMs) pose to democratic societies through their persuasive capabilities. We expand upon existing research by conducting two survey experiments and a real-world simulation exercise to determine whether it is more cost effective to persuade a large number of voters using LLM chatbots compared to standard political campaign practice, taking into account both the "receive" and "accept" steps in the persuasion process (Zaller 1992). These experiments improve upon previous work by assessing extended interactions between humans and LLMs (instead of using single-shot interactions) and by assessing both short- and long-run persuasive effects (rather than simply asking users to rate the persuasiveness of LLM-produced content). In two survey experiments (N = 10,417) across three distinct political domains, we find that while LLMs are about as persuasive as actual campaign ads once voters are exposed to them, political persuasion in the real-world depends on both exposure to a persuasive message and its impact conditional on exposure. Through simulations based on real-world parameters, we estimate that LLM-based persuasion costs between \$48-\$74 per persuaded voter compared to \$100 for traditional campaign methods, when accounting for the costs of exposure. However, it is currently much easier to scale traditional campaign persuasion methods than LLM-based persuasion. While LLMs do not currently appear to have substantially greater potential for large-scale political persuasion than existing non-LLM methods, this may change as LLM capabilities continue to improve and it becomes easier to scalably encourage exposure to persuasive LLMs.