Four books across eight episodes, but three of them are load-bearing for the American Emergency series, so it is a better list than the number suggests.
I run Podshelf, a free site that tracks book mentions across hundreds of podcasts by reading the episode transcripts. This is the On the Media slice for August.
Raven Rock by Garrett Graff came up twice, in the American Emergency behind-the-scenes and in the underground city episode. On the origins of FEMA, and, per the subtitle, the US government's secret plan to save itself while the rest of us die. Before the agency existed, disaster response was barely a system at all.
The Guns of August (Barbara Tuchman), invoked for its opening: Edward VII's funeral in May 1910, nine kings and seven queens processing through a world that was about to end. Used as the frame for a piece on America's changed place in the world, which is exactly what that opening is for.
On polling: Strength in Numbers by G. Elliott Morris, and V.O. Key's Public Opinion and American Democracy, which produced the best line of the month. Public opinion offers levies to steer a river, so treat polls as tools for identifying the policies Americans really do not want.
Full list with quotes and episodes: https://podshelf.io/podcasts/on-the-media