I get the feeling you have something else in mind ...
Now there's a Bugs Bunny cartoon I never saw!
I wonder if you can link us to it somehow, to a plot summary or at least it's title anyway.
I wonder why none of the Warner Brothers' showcase shows I ever saw never showed it, and how many others there are I never heard of.
I can guess; between violence that caused some old chestnuts I saw in full as a kid to be censored for that (King Ferdinand whacking Christopher Columbus's "round" head flat with a mallet for instance

) and some quite casual racism, lots of classic cartoons are censor-worthy--it makes me wonder just how blatant the ones that weren't shown in the late Sixties and 1970s were.
Or of course maybe someone with a limited budget who had to choose the top 20 or so from hundreds just decided they'd picked the most cost-effectively funny ones?
I do want to know why Bugs Bunny is sawing off Florida the long way here.
But to the topic--I too have to wonder why the heck anyone would feel a need for a Florida canal, except of course as offered as a fortification moat. And even that seems incredibly far-fetched; whoever wants to defend some line across the southern peninsula would hardly be motivated to offer to have it double as a canal. A land-based Maginot Line sort of thing seems more likely.
A Spain-wank uberpowerful Spanish Empire holding not only South Florida but Cuba and many other Caribbean islands too might give someone holding as far south as Jacksonville and some point not too far west on the OTL panhandle coast the motive I guess, not for defense but for transiting when the aggressive Spanish have blocked the sea lanes--but such a powerful Spain would probably push the boundary far to the north, whereas a nation to the north rich enough to contemplate the tremendous amount of digging involved would as someone said probably just try to settle the matter by taking South Florida (and Cuba while they were at it, perhaps).
Assuming people are reasonable about freedom of the seas there's plenty of room between the Keys and Cuba for everyone's peacetime merchants to pass freely, and there aren't a lot of ports unduly "shadowed" by the peninsula to make a canal look at all cost-effective. You can still make New Orleans without a lot of miles added, and Mobile and Pensacola just aren't that important.
And even now, with all the growth the state of Florida has enjoyed since cheap air-conditioners were invented, the land, even the coastal beach land, between Panama City and somewhere north of Tampa remains almost utterly deserted. I know, I spent about 1/3 my childhood living near PC since my Dad's career revolved around Tyndall AFB, and graduated high school there in Bay County--I know just what a wasteland that stretch of Gulf Coast is. I suppose there might have been some growth there since, but last time I looked at a satellite picture of Earth's night lights from space that whole stretch from Apalachicola (pop well under 3000 as of 2005!) to, I dunno, Steinhatchee or whatever, way south on the east side of the peninsula, looks like black open ocean. I've never known just why; perhaps there aren't any white sandy beaches there as there are farther west and the coast is muddy estuary swamp?
It just isn't that desired a goal, for whatever reason.
To go back to the idea of fortifying the north border--the first timeline that comes to mind where that project could have both motive and funds strikes me as Dathi Thorrfinson's "Canada Wank," which appears to have unfortunately died forever.



There, a much stronger British North America almost encircles a USA curtailed mostly in the northwest--after two wars it stops at the Mississippi (or points considerably farther east, up toward the Great Lakes). Also, New England seceded during the first war (War of 1812). There hasn't been a north-south Civil War yet and possibly never will be one.
There, Florida is not British but remains Spanish--however both British Louisiana and Spanish Florida get a lot of fugitive slave refugees; by the 1850s African-Americans have been living in both for generations and have fought to defend both from Yankee attempted conquests. I envision those Afro-Spanish subjects in West Florida serving as the settler population that has built itself up quite a lot by now and if Spain can afford the funds, they'd want a Maginot Line of their own against the southern tier of states.
But a canal from St. Augustine to Mobile is just plain silly. It would be a line of bunkers and forts and perhaps some long walls, maybe river-fed moats. Not a damn oceanic canal!