That was Bugs rather than Daffy, but yes, Looney Tunes is one of the main theories about how "nimrod" came to shift meanings, although it isn't the only theory. Something to keep in mind is that Looney Tunes had a lot of references to contemporary pop culture that Looney Tunes itself ended up outliving by nearly a century now, so in that way Looney Tunes has ended up being kind of like the modern Shakespeare, where a lot of people say that Shakespeare was the originator of a lot of words, but the situation is really more like Shakespeare's works are just the earliest surviving written examples of those words.

Ask me from my armchair, looking at Wiktionary's etymology section for "nimrod", and I'd say that most of the theories about how "nimrod" came to mean "idiot" probably have some truth to them. Namely, long before Looney Tunes — centuries before, even — there were already a number of words for "idiot" that happened to start with the letters ni-, like ning-nong, ning-nang, nincom, nincompoop, ninny, ninnyhammer, nitwit, the likes. So it doesn't seem far fetched to me that people would start using "nimrod" as a euphemism for any of these terms, maybe as early as the 19th century if Col. Nimrod Wildfire in James Paulding's The Lion of the West (1831) is anything to go off of; and because Nimrod was a great hunter, then this euphemism would've originally been used as a tongue in cheek way of saying that somebody's a ""great"" hunter, either literal, of animals, or figuratively, of love interests, or even of both. This leads to a lot of ambiguous uses of the word "nimrod" (Looney Tunes being one example, Great Magoo (1933) being an example predating Looney Tunes highlighted by the OED), and somewhere along the line, the euphemism gets wholly conflated for what it's substituting, as seems to so often happen with euphemism. But IMO this shift was probably as a culmination of a bunch of unwritten conversations between average people, and several works of mass media, of which Looney Tunes just happens to be the most popular example that stood the test of time.

But, as said, this is just me from my armchair.

{Cēterum|Furthermore} {cēnseō|I think} {iūs auctōris|copyright} {esse dēlendum|must be destroyed}.