Barack Obama sometimes pronounces the word divisive with a short i in the second syllable (similar to permissive or dismissive). In his March 2008 speech on race, he says it twice in a row that way, at about the 7:50 mark. (He also uses it in the traditional long--i pronunciation, a la incisive, at 5:44.)
There has been a fair amount of grumbling about Obama and various members of the chattering classes using the “divissive” pronunciation, much of which assumes they are aping the British. That is understandable, given the way the Brits say “vittamin” and “dinnasty,” but it is not correct. The OED lists only one pronunciation for the word: with a long i. A lengthy discussion at the Washington Monthly website (which descends to personal invective at the end in a predictable, almost ritualistic manner) suggests the short-i is an American regionalism, found in New England and the Midwest. (Apparently former South Dakota Senator Tom Daschle said it that way.)
Regionalism aside, to my ears the “divissive” pronunciation comes off as an affectation, that is, a case of saying something differently for the express purpose of saying it differently, similar to pronouncing the word “negociate.” One of the first people to gripe about it was Charles Harrington Elster, in his 1999 “The Big Book of Beastly Mispronunciations: The Complete Opinionated Guide for the Careful Speaker.” His target was another president, George H.W. Bush, who apparently said “divissive” in his inaugural address in 1988. Elster asks rhetorically: “Was this just a venial bit of Ivy League snobbery, or was the president letting fly with a beastly mispronunciation?” I vote for the former.
notoneoffbritishisms.com 
I’ve always said it with a short “i” and I grew up in California (and I’m a lot older than Obama).
I’ve never said the word one way or the other.
“Short i – long i” This how wars start.
I’m a native Brit, but have only ever heard the “divissive” pronunciation in the USA.
So I agree that this isn’t a NOOB.
I’d never heard it before in my life (fellow Brit), so seconded!
NOOBs aside, this Cornellian who’s lived in Texas now for 32 years never really noticed President Bush’s “Ivy League snobbery,” since his “nucular” drowned out all his other mispronunciations and made me cringe every time I heard it.
Wrong Bush…Nucular Bush was the son, divissive Bush the dad…
One theory suggests that Bush’s howlers were not caused
by regional dialects but rather by a neurological condition
brought on by years of heavy drinking.
Not to be divisive, take a look at the article on Hemingway in today’s (3/19) Slate. You’ll find the use of “twee.” in the copy.
To add to the testimonies above, honestly this is not a NOOB, and needs to be struck off the list. It simply does not exist over here, and if it did it would sound like an Americanism.
With pronunciations like these I think there’s sometimes another force at work, though it’s hard to describe it. I grew up assuming the word “controversial” was pronounced “con-tro-VER-shul”, but in the early ’80s I suddenly began to hear news anchors (i.e., news presenters to you Brits) pronouncing it “con-tro-VER-see-all”. This outrageous detour lasted several years and then, unless I’m mistaken, quietly disappeared. Why did it happen and what kept it going? No idea.
More recently there’s been an extraordinarily annoying trend to insert the superfluous word “of” into phrases such as “not that big a deal” or “not that exciting a movie”, making them “not that big of a deal” and “not that exciting of a movie”. I’ve even seen such constructions in the New York Times. So when it comes to pronouncing negotiate as negociate, I think it’s simplistic to dismiss it as “saying something differently for the express purpose of saying it differently”. There are weird forces at work on language, and many of them have nothing to do with our innate tendency to be pretentious.
‘Divissive’ has come in recently in Britain, usually in the mouths of those business types who deploy Managementspeak. That suggests, to my biased ears, that it probably came from the US, along with the business schools. To those same ears it also sounds ghastly – and pretentious.
But we’ve endured an awful lot of this over the years. One from 10 or 20 years ago, which seems to have stuck, is to say ‘inherrent’ (as in ‘heron’) rather than ‘inherent’ (as in ‘here’).
As a retired, formerly longtime employee of an American Computer company, I have learned to loathe “Managementspeak” also. Some of the phrases that annoy me are “oh, by the way”, and “reach out to” (as opposed to “call” or “contact”). I also really dislike the new verbs that people are using, like “plating” your food, and “disrespecting” your name. The use of these things persist and grow however, and I guess it’s part of the normal evolution of the language. I think it’s human nature to resist the things that are different now than the way we learned them.