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.