Most widely-used measures of politicians' ideology are based on the idea that 'true' ideal points can be inferred from behavior such as voting records and campaign donations. However, these measures have been widely criticized for their lack of correspondence to popular understandings of ideology, frequently casting notorious firebrands as moderates and vice versa. We argue that this is a feature, not a measurement bug: political communication is strategic, and politicians deliberately choose to speak in a way that does not match their true ideology in order to affect voter perceptions. In this paper, we explore this claim in two parts. First, using a novel measurement strategy that integrates the possibilities of modern LLMs with statistically principled scaling approaches rooted in WordFish, we estimate a K-dimensional measure of rhetorical ideology for each member of the 119th US Congress based on an array of data sources encompassing both direct evidence such as campaign ads or newsletters and indirect measures of media portrayals across digital and broadcast media. Second, we validate this measure against original survey estimates of voters' perceptions of their representatives' ideology. In doing so, we provide an empirical estimate of the limits of 'cheap talk' in democratic politics: the extent to which voters can exploit a lack of voter information to reap electoral rewards by presenting themselves as holding an ideology that diverges from their observable behavior.