I’m on the east coast, and I’ve heard this phrase used–usually in “off like a herd of turtles”-- only twice, both times from PNW type folks, one from Seattle, and one from Portland.
Googling around, I found a number of sites using the term, but no info on the origin. I guess you could say no site with a cite of the first sight. Anyway. . .
Anyone with any info on the origin of this phrase?
I heard it from my father growing up in rural PA. It goes back at least 40 years, and PA is pretty far removed from the PNW.
I hear it all the time from my Dutch/Canadian step father who grew up in rural Ontario and now lives in Montreal . . . I get the impression it’s pretty wide-spread.
My father used to use that phrase (in southern Iowa), whenever we’d start a trip. Of course, he’d always say “We’re off like a turd of hertles.”
My dad also began each trip (according to my memories beginning in the mid-1950s) with either “We’re OFF, like a herd of turtles” or, more rarely, “We’re OFF, like a hoid of toitles”–a tradition I faithfully carry on.
He was raised in Indianapolis and I was raised in suburban Detroit.
My dad, born and raised in Texas, used this phrase for as long as I can remember (as well as intentionally spoonerizing it to “a turd of hurdles”). I didn’t know until I read this thread that it was used by so many–I always thought it was something he made up!
I, of course, use this saying fairly often myself–ah, how great traditions are made! 
My mom used to use that phrase all the time when I was a kid; we lived in St. Louis, and she grew up in Michigan and the Bay Area.
Looking like the consensus is that it’s not a regional expression. 
I grew up in MA and both my parents grew up here also. I have heard both my parents use this phrase and I use this phrase now as well as my daughter. And now… I’m off like a herd of turtles!
I have heard it used and used it in my western NY/southern Iowa family for close to 50 years.
My family also uses ‘* at the crack of noon’ to indicate a later start than desired or that someone stayed in bed past normal wake up time. [poking fun at the phrase ‘to get up or whatever at the crack of dawn’. ]
"Thundering like a herd of turtles’ I first heard this from a guy in New York state about 15 years ago. Made me giggle then and I still think it’s funny now.
I first recall hearing this as a teenager in PA in the 70s. Also the alliterative phrase, flock of flying turtles.
Heard it in the 60’s in the Washington, D.C. area, and afterwards in the Kansas City area.
Origin? I don’t have a clue. What’s the origin of “like herding cats?” What’s the origin of “went over like a lead balloon?” I suspect these are so commonplace and widespread that no one can pin it down.
My mother used “We’re off like a herd of turtles”, too; she was from eastern Wisconsin.
How about “a herd of zombies?”
My mom says it. She’s a life-long Upstate New Yorker.
I’m from the NY/NJ area and I’ve heard it, too.
Half an hour of looking in Google Books and all my newspaper databases says it’s a much more recent phrase than I would have thought.
Starts being used in the 1940s.
Well, it was used at least ten years ago, when the thread was brand new. 
My mother always said it, and I’m 65. She was from Portland.
Grew up in West Texas. Lived as an adult in Albuquerque and Honolulu. Never heard it.
I live in northeastern PA, and I first heard it a few years ago from a co-worker. I’ve occasionally used it myself when it takes too long to complete a seemingly simple task.
My father’s been using that line as far back as I can remember - from at least the late 1970s - and I’m sure well before I came along.
Southeastern Massachusetts, location-wise.