Well, Curly did say it.
From “Idle Roomers” (1943):
Still, I will not be surprised to see that this came originally from an old vaudeville routine.
Having watched “Are You Being Served” way too many times over the years, I don’t recall Mrs Slocum ever saying “I resemble that remark” (although maybe she did once, anything is possible).
Her catch phrase was “And I am unanimous in that”, along with various innuedos concerning her “pussy” (“Tiddles” I think, although she did get a new cat later in the series) and stories about her pub outings with Mrs Axelbee.
I think I first saw it on MASH, so my first guess would be Groucho.
I’m 99% sure that Groucho never said it in any of the movies, although the last few had lines that were equally stupid. He might have said it on You Bet Your Life, but I doubt that too. Nothing comes up in a search, except people who attribute it to him with no source or cite.
Let’s face it. The line is Three Stooges level humor. That alone is proof that Groucho never said it.
The first time I heard it was Duck’s Breath Mystery Theater
Curly used the line in “Idle Roomers”, filmed in 1943. Does anyone know of an earlier use?
Zombies don’t resemble any remarks!
Why, you. I oughta…
Zombie thread and all that, but I agree – the expression has always struck me as an extremely feeble and un-funny “funny”.
Zombie thread blah blah…
I can’t believe I’m the first contestant to identify Quick Draw McGraw (1960’s Hannah-Barbera cartoon) as an utterer of the phrase. “Now hold on, thar! I resemble that statement!”
I wouldn’t rule out Popeye. He was a master at mixkin up his words. 
I confess to never having heard of him before. No relation, I suppose, to Wallace and Gromit’s villainous penguin, Feathers McGraw…?
Similarly, every time I hear or read the line “I am serious, and don’t call me Shirley!” I think fer sure that’s a Groucho line. I’m always surprised to see that the first use, apparently, was in Airplane!, by Leslie Nielson, 1980.
Quick-Draw McGraw was an anthropomorphic horse of Hanna Barbera, who walked upright on his hind legs and was sometimes shown riding an actual horse-like horse. Like Huckleberry Hound and Yogi Bear, he had a sidekick – a little burro named Baba Looey.
I would just like to point out that, after 10 years, I don’t really care all that much.
Can’t speak to the comic strip, but I’m pretty familiar with all the original Fleischer-era animated Popeyes, and I don’t recall ever hearing him say this.
Pardon the sidetrack, but as we’re not likely to see a “favorite Popeye mutterings” thread, I’ll post mine here.
In “I Never Changes Me Altitude,” Popeye and Bluto are engaged in a mid-air fight with their respective small planes. Bluto gives Popeye’s craft a whack with the wings of his plane and knocks him out of the open cockpit.
Popeye slides down his now-vertical wing, avoiding being hurled into the air by clutching at the skin of the plane, which is gradually separated from the framework by his downward momentum. He responds by saying “This is terrible, this is terrible (tearable).”
The sailor then gets his bearings, and clambers back up the still-vertical wing, patching up the skin as he goes. His positive, resourceful outlook returning, he mutters, “Hmm, just need a little mucilage on the fuselage.”
All hail the great Jack Mercer, who apparently ad-libbed many of Popeye’s mutterings on the spot as the soundtracks were being recorded onto the already-finished animation.
Baba Looey was a burro? I always thought he was supposed to be a calf or small bull. “Queecksdraw, eet’s the golden spike!”
Thanks, people. I have to wonder whether there might be any “crossover / borrowing” with the Glaswegian strip-cartoon which flourished some three-quarters of a century ago, hero thereof Lobey Dosser. Glasgow is IMO one of the world’s delightfully insane places: there was a long-running feature by a local cartoonist, which surreally mixed up Glasgow, and the Wild West. Lobey Dosser was the Sheriff of Calton Creek (Calton being a notorious Glasgow bad neighbourhood) – he rode a two-legged and permanently upright horse called El Fideldo, and had innumerable strange adventures, accompanied by much spectacularly-awful punning.
In “The Jeep,” Olive Oyl opens the door while an oblivious Popeye continues knocking on her head. When he realizes what he’s doing, he mutters “I didn’t know I was knocking on a Dumb Door-a!” Later, Popeye is hunting for a missing Swee’pea, and checks behind a painting, muttering “Searchez la frame!”
Izzat So?
Missed the first one but remember the second one well! A classic.
Another just occurred to me…in “Ghosks is the Bunk,” Bluto rigs up an abandoned house with haunted-house type gags, then lures Popeye and Olive there to have some fun. He gets the better of them for a while, until they discover Bluto behind the scenes working the gags.
From this point on, the tables are turned…especially when Popeye discovers some “invisible paint” that causes him to disappear when applied. As he’s slathering it on his upper limbs, he mutters “Well, farewell to arms.”