Not exactly. There's a better argument that the 1918 pandemic was a serious but short-lived and largely forgotten episode in the progressive era and failed to turn the tide against a rising right-wing correction.

The flu pandemic did not occur in a vacuum, as the Great War kept raging through Europe. The flu was unusually lethal for some reason (perhaps cytokine storms or aspirin poisoning) and swept through populations of soldiers and civilians swiftly, though it largely subsided after the deadly second wave in autumn 1918. One theory is the pandemic was "forgotten" quickly because various outbreaks of diseases like cholera, diphtheria, typhoid, and yellow fever also spread during the early 20th century, as well as the fact that Western media (except for neutral Spain) largely suppressed information about the Spanish flu for wartime propaganda purposes. Another theory is a sort of "collective PTSD" that pushed survivors to avoid discussing the experience, akin to the shell shock of many veterans.

But perhaps the most important fact is the 1918 pandemic coincided with the end of WWI and was thus overshadowed domestically by much of the geopolitical peace negotiations. US President Woodrow Wilson embarked on a nationwide tour to boost support for his League of Nations idea, but the Senate ultimately rejected the treaty, and he served out the term as a sickly lame duck. Thus the 1920 election became a referendum on foreign policy and isolationism, the so-called "return to normalcy." Republican candidate Warren Harding defeated Democratic nominee James Cox in a landslide. The American people seemed weary of international obligations and chose Harding's message of "America First," signaling a return to control of the US by American institutions or national sovereignty.

Of course, in the US, unlike Russia and parts of Western Europe, the 1918 flu influenced public health by spurring reforms in data aggregation and employer-based health insurance plans, as well as the rise of epidemiology as a study. But for various social and political reasons, the specter of the pandemic seemed to not be memorable or powerful enough to overcome a general conservative backlash in the 1920s, sparked by foreign policy sentiments, that precluded proposals like nationalization of insurance firms or universal healthcare coverage.

Sources

Barry, John M. (2004). The Great Influenza: The Epic Story of the Greatest Plague in History. Viking Penguin. ISBN 978-0-670-89473-4.

Morens DM, Taubenberger JK, Harvey HA, Memoli MJ. The 1918 influenza pandemic: lessons for 2009 and the future. Crit Care Med. 2010;38(4 Suppl):e10–e20. doi:10.1097/CCM.0b013e3181ceb25b

Trani, Eugene P., Eugene P. Trani, Eugene P. Trani, Virginia Commonwealth University, and Virginia Commonwealth University. “Warren G. Harding: Campaigns and Elections.” Miller Center, July 25, 2018. https://millercenter.org/president/harding/campaigns-and-elections.

“How the 1918 Flu Pandemic Revolutionized Public Health.” Smithsonian.com. Smithsonian Institution, September 27, 2017. https://www.smithsonianmag.com/history/how-1918-flu-pandemic-revolutionized-public-health-180965025/.