In the US military the terms I have come across are TAD or TDY for Temporarily Assigned Duty. We love our TLAs.
QFT! 
I think (perhaps someone can confirm) that:
For that subset of Americans who pronounce box so as to sound (to BrE ears) like they are saying ‘baax’…
A typical BrE pronunciation of box may sound something like ‘borx’ or maybe ‘bawx’
(these are inexact transcriptions of the sounds, and I can’t be bothered to try to figure out the IPA)
/bɑks/ for US
/bɒks/ for UK (Received Pronunciation)
This is also the reason why the name Bob Loblaw is, supposedly to Americans, meant to resemble Blah Blah Blah but to my Kiwi ears it really does not.
Well, we like to pretend to think that when a merkin says “I’m rootin’ fer Dallas” or whatever, that they are having sex for them in some way.
If you voluntarily choose to root for the Cowboys, you’re definitely getting fucked every season.
You certainly need to be cautious about telling an Australian that you’ll be rooting around in your drawers.
American English speaker here, from SE Louisiana. You are generally correct. As far as I can determine, the percentage of Americans who pronounce box to sound to you like ‘baax’ approaches 100%. It’s far, far more than a subset.
We wouldn’t use an ‘r’ to phonetically spell what British box sounds like to Americans. Almost all American dialects are rhotic – pronouncing a distinct ‘r’ – and this ‘borx’ would be taken as a very different thing. ‘Bawx’ would be about right, except I know that the vowel in British box is (generally) briefer than the vowel in near-rhyme words like hawks and squawks.
Around here, if one wanted to heavily overdo a generic British accent, one could pronounce the ‘short o’ words with American ‘long o’s’. ‘Tope of the Popes’ instead of Top of the Pops. Such a pronunciation would be understood here – as an imitation of a British accent – as off a bit, but not by much. British listeners, of course, would find it all kinds of wrong 
I remember one time the Cowboys were losing and the commentator said their coach was pissed. My first thought as a British English speaker was no wonder they’re bloody losing 
That’s nowhere near true. We do not pronounce it that way in the northeast. It seems to be a southern and Midwest thing.
Yes as a Brit I’d say New Yorkers, Bostonians and so on may say it more like ‘bawx’??
I just had reason to look up details of the history of Glasgow and there was mention of an incident involving a bin lorry. It took me a couple of seconds to decrypt that into garbage truck.
To my experience, yes, there are some American English dialects that would be exceptions. In my head, I can readily hear, say, Emeril Lagasse’s (Fall River, MA) speaking “short o’s” in some words like box as “bawx”.
I believe that Brooklynese has some similar pronunciations. Unsure about other northeastern US cities like Philadelphia, Hartford, Providence, etc.
In your estimation, is this pronunciation still getting passed down to young people in the northeast, or is it fading away?
Did you mean something else by “baax”? To me that would rhyme with fax, a pronunciation I associate with the midwest and south. In the northeast/New York region I have only ever heard box to rhyme with socks.
What is fading away (or actually has faded away ) is the old-fashioned cartoonish Brooklyn accent where oil was pronounced like earl and toilet was terlet.
I don’t recall ever hearing that added w in box - but I still hear tawk and wawk.all the time.
Oh – I see.
“Baax” was originally Mangetout’s usage and I was just using it while responding to his post. Since Mangetout is British, I took his “baax” to be equivalent to my “bahx” (with a conversational-speed version of the “open up and say ‘ah’” vowel). Translated into my own dialect (New Orleans area speech), in my own headspace I was rendering Mangetout’s take as:
"Here in the UK, most of us say something close to US “bokes” … but not quite that. Whereas most Americans seem to say “bahx” … with the vowel in “bah, bah, black sheep.”
This is where not using IPA gets us into a little bit of trouble. All the same, it can be an interesting exercise to get other English speakers to understand what you’re going for without using IPA – just so long as we recognize that we’ll often fall short in precisely communicating the pronunciation differences.
…
FWIW, down here, box and socks also rhyme. Locally, both use the “open up and say ‘ah’” vowel mentioned above – that’s what we learned as “short o” in elementary school.
This and thousands of other examples show why the International Phonetic Alphabet is indispensable. By this point, refusal to learn the few symbols needed for English is an expression of obstinate anti-intellectualism.
Look, I’m not saying it people shouldn’t learn it - but I don’t think it’s “obstinate anti-intellectualism” to not learn an alphabet that a person might use a couple of times a year.
In every other field of knowledge, Dopers accept that accuracy in facts is necessary. Discussions of, say, math or physics assume that anyone participating will accept use of standard terminology and notation. Nobody complains that math formulas are too hard to learn. Even though the few IPA symbols needed for English are infinitely easier to learn than physics math. If you’re going to participate in a scientific discussion, you’re expected to know the basics of the science. Linguistics is a science too, don’t forget.
Only when it comes to English phonology do Dopers start to believe, in the words of Asimov, that “my ignorance is just as good as your knowledge.” It’s aggressive ignorance.