Mr. Aiona is hoping to take over for the current GOP governor, the term-limited Linda Lingle.
The races on paper were not supposed to be competitive. Democrats have held the House seat for all but four years since it was first carved out in 1971, including 11 terms for Mr. Abercrombie before he quit. Before Mrs. Lingle was elected in 2002, Democrats had held the governorship for 40 years.
The candidates said the latest poll numbers would have no impact on their campaigns.
"Forget about these polls," Mr. Aiona told KHON. "It doesn't matter. What matters is the ideas that we have. I don't care if it's 20 points the other way, you should be excited."
Mr. Abercrombie said, "We've learned a long time ago that the only poll that matters is on Election Day."
In a sign national Democrats are not taking the races for granted, Mrs. Hanabusa is also getting a boost this week from Washington's Democratic Congressional Campaign Committee, the national party committee charged with helping Democratic House candidates. The DCCC is running a new negative ad that accuses Mr. Djou of voting against federal funds for Hawaii schools and teachers.
The ad has been called "an absolute smear campaign" by Hawaiian GOP officials. Mr. Djou, in an interview with the Honolulu Star-Advertiser, defended his vote against the $26 billion package of aid to state governments passed this summer, saying it was unfair to ask Hawaii to "bail out" less fiscally responsible states.
Mr. Djou's bid, like a number of Republican campaigns over the past year, is getting a jolt of activism and energy from the anti-spending "tea party" movement.
The one-time Honolulu city councilman and former state lawmaker earned tea party support last spring, but since then Mr. Djou has de-emphasized his connections to the movement.
But his latest ad airing this week takes up a favorite tea party theme, accusing his opponent of underestimating the scope of wasteful government spending. Mrs. Hanabusa's campaign immediately cried foul, claiming the snippet of film quoting her in the ad was taken out of context.
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