It appears that "in the hurry" was more popular in the late 19th century. See http://corpus.byu.edu/coha/?c=coha&q=40052682. Also, see the following Google Ngram:
(Google Ngram in the hurry, in a hurry)
So most usage will be like "I'm in a hurry". Do note that's informal and conversational.
The rest of this post will focus on "in the hurry" because I think it's getting a bad rap. First consider this:
- In my hurry to evacuate, I forgot my wallet. [Ok.]
- In a hurry to evacuate, I forgot my wallet. [This doesn't sound right to me.]
- In the hurry to evacuate, I forgot my wallet. [This sounds better to me, but I think it's a bit unbalanced.]
- In the hurry to evacuate, two people got hurt. [Ok.]
#1 is specific to the individual's effort. #2 doesn't sound right to me but it might be ok. #3 may suggest a general hurry of people, perhaps some sirens and confusion; my problem with it is a matter of style: it's unbalanced between the abstract hurrying and the specific person. #4 sounds good and has balance since it's talking about the hurry in general along with a related general fact.
Now consider this:
- In the hurry of modern life, it's difficult to make time for what really matters.
While ok, this example above may sound a little forced. I think because the word "hurry" is doing all the work of explaining itself. But I think it's grammatically ok. Compare to the following quote, which sounds perfectly fine to my AmEng ears:
My quick review (google ngram, COCHA) suggests that in written form, contemporary usage of "in the hurry" is mostly found in fiction. That's a good clue that it's informal, conversational, or nonstandard English. And there seems to be a few people (google search, social media, comments) who will simply say "I'm in the hurry" or "I'm in the hurry to...". So "in the hurry" is now mostly informal/conversational as part of a non-standard dialect of English.
But I do think it has a proper place in spoken usage. Consider the following:
Captain Birk knew that as soon as the sun set on this planet, the Dwelvers would be coming out and combing the desert for anything alive. That magnificent red giant was inching it's way to the horizon. He reached his hand out. Five fingers to go.
Tanner saw the captain and knew what he was thinking. As he lifted one of the pods and threw it into the back of the truck, he shouted to the rest of the squad, "Ok men! Let's get this wrapped up! I'm in the hurry to get this over with and get back to the ship!"
To me, "in the hurry" works better than "in a hurry" in the above passage. "I'm in a hurry" sounds more urgent and immediate than "I'm in the hurry".
I think we're all suffering a bit of "it does/doesn't sound right to me" syndrome, which is probably overriding some fundamental grammatical correctness issues. Someone more academic may shed some more light on this, perhaps in another answer or a comment.
That's all for now. I'm in the hurry to get to bed. :)