I'm curious as to if there are records of the backlash that I would expect to hear from a Presidential statement like that. Has anyone investigated and have insight into how the printed media and political adversaries responded to this speech?
Here's an excerpt from an FDR biography that, in my opinion, paints a pretty good picture as to what was going on at the time surrounding his Four Freedoms speech. It includes a couple of references to the opposition: link
The tricky thing about finding backlash about the speech itself is that it was so overwhelmingly popular. As the years went on, the speech, and FDR, only became more popular. This article reflects on the speech and some of the reactions, both at the time and through the lens of hindsight: link
The big thing to remember about the speech is that it was delivered only a few months before Pearl Harbor. At the time the only real complaint about the Four Freedoms speech was that it felt like FDR was leading the U.S. into war, and even that complaint was more about FDR's policies rather than the speech itself. Obviously, those complaints were quickly silenced after America was bombed in Pearl Harbor.
I hope that answers your question! Essentially, the speech itself was a big hit and what little opposition it had was more towards FDR in general, rather than the speech itself.