Former Rep. Ed Case (D) is not wasting any time in the yet-to-be scheduled special election to replace Rep. Neil Abercrombie (D), who is resigning next year. Case announced this week that he began airing a television ad to boost his special election bid.

Case was also the first to announce that he is running in the special election, even though it’s unclear when Abercrombie is departing or when the contest will be scheduled. State Senate President Colleen Hanabusa (D) is also running in the winner-take-all contest, along with Honolulu City Councilman Charles Djou (R).

It’s unclear when the special election contest will be held, and complicating matters is the fact that the state faces a major budget crisis. Local reports have said the office of elections was already scrambling to figure out how it could afford to pay for the regularly scheduled primaries in September 2010. Local officials are considering cutting costs by holding the special election via the mail, which was recently used in a special contest for a state legislative seat.