To add to the intrigue, President Obama, who grew up in Honolulu, has made a rare intervention in a Democratic primary. He has endorsed Mr. Schatz, who supported him in the 2008 Democratic presidential contest; Ms. Hanabusa and Mr. Inouye backed Hillary Rodham Clinton. As a result, the primary vote is shaping up as test of clout between a living president and a dead senator.

Mr. Abercrombie’s primary opponent is David Ige, a longtime member of the State Senate. In a poll released this month by Honolulu Civil Beat, an online news organization, Mr. Ige led Mr. Abercrombie 48 percent to 37 percent, a particularly stunning result, given that the governor’s spending on television advertising had dwarfed that of Mr. Ige. The news organization said it had been so surprised to find Mr. Ige with a double-digit lead when it first polled in May that it polled again in June.

The conflict has the requisite generational and ethnic political factors that are integral here. Ms. Hanabusa and Mr. Ige are, as Mr. Inouye was, Japanese-American. Japanese-Americans — the third-largest ethnic group in the state, with 23 percent of the population — are known for voting in disproportionate numbers.

If the act of defying Mr. Inouye was not enough, Mr. Abercrombie also suggested in an interview with The Los Angeles Times in April that the deathbed letter dispatched by Mr. Inouye was a fabrication. Mr. Abercrombie later apologized to Mr. Inouye’s widow. But Democrats here say the remark might motivate Japanese-Americans in a way Mr. Inouye would never have been able to do from the grave.