There's actually a lot of interesting information in other places on the web about this topic, so I thought I'd post an answer summarizing some of it.
Apparently, /dɪˈvɪsɪv/ ("divissive") is more common in Canada
According to the post "The great divide" by Katherine Barber on her blog Wordlady,
At the Canadian Oxford Dictionary we found that "di VISS iv" is in
fact the most common pronunciation in Canada for this word.
This preference for "di VISS iv" seems to be unique to Canada.
Dictionaries from other countries give their pronunciations of the
middle syllable in order of frequency:
NZ and Australia: VICE , VIZZ
US: VICE, VISS, VIZE, VIZZ
Canada: VISS, VICE, VIZZ, VIZE
The pronunciation "divissive" is uncommon in British English
Ben Yagoda's blog Not One-Off Britishisms also has a post about this pronunciation.
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.)
There are some interesting comments that seem to support the above generalizations in this Straight Dope thread, "How do YOU believe the word "divisive" is correctly pronounced?"
05-22-2012, 08:21 AM FloatyGimpy
I'm Canadian, I've never heard it pronounced with the "eye" sound.
05-22-2012, 04:56 PM Teacake
British. Div-EYE-sieve. I've never heard it pronounced the other way.