HONOLULU, OCT. 31 -- In ordinary times, and under ordinary circumstances, Sen. Daniel K. Akaka (D-Hawaii) shouldn't have any reason to worry.

He is a Democrat running in one of the country's most heavily Democratic states -- one of only six states carried by Jimmy Carter in 1980, and one of the 10 that Michael S. Dukakis won in 1988.

Akaka is also a political veteran, a native Hawaiian who has served seven terms as one of the state's two House members in Congress. And this year he is running for Senate with the added boost of incumbency. He was appointed to the seat last April following the death of Hawaii's popular junior senator, Spark M. Matsunaga (D). Tuesday's election is to fill the remaining four years of Matsunaga's term.

But these are not ordinary times for politics in Hawaii, where ethnicity, gender and a rapidly changing electoral base are making this Senate race one of the most closely contested in the country.

Akaka's Republican opponent, two-term Rep. Patricia F. Saiki, is Japanese American, and she is cutting deeply into what has long been considered the Democratic Party's core constituency. Her strong showing has made national Republicans cautiously hopeful of capturing a normally "safe" Democratic Senate seat while the hard-fought campaign has underscored how the influx of more conservative Caucasians from the mainland could forever change the face of the Aloha State.

"I've always said that by 1994, this state will be up for grabs," state Republican chairman D.G. "Andy" Anderson said. White mainlanders, he said, now account for about 34 percent of the electorate "and they're growing every year." The problem, he and other political analysts here agree, is that these newcomers often do not vote in off-year elections.

The latest poll, published today by the Honolulu Advertiser, shows the Akaka-Saiki race a virtual tossup, with Saiki slightly ahead 45 to 42 percent with 11 percent undecided.

Most striking about the poll findings is Saiki's strong showing among Caucasians, who back her by a 58 to 33 percent edge. In addition, she is winning 47 percent of the male vote and 44 percent of the women.

Saiki is also benefiting from a large crossover by traditional Democrats -- most of them Japanese Americans who appear to be abandoning their party to support one of their own. The poll showed Saiki winning 38 percent of the Japanese-American vote, with an additional 16 percent of these voters undecided. Japanese Americans account for about one-third of the electorate, make up the core of the traditional Democratic vote and usually turn out on Election Day in excess of 80 percent.

"Without question, you cannot ignore that. This bloc of voters is extremely important to our campaign," said Akaka's campaign manager, Kam Kuwata. "She cannot take them for granted because of ethnic identification, and we cannot take them for granted because of their party identification." Both campaigns have been concentrating their final efforts on heavily Japanese-American districts, mostly in central Honolulu neighborhoods such as St. Louis Heights.

Akaka, sensing his campaign is in trouble, has been stressing his Democratic roots. His television commercials proudly tout his endorsements from the National Education Association and other groups that traditionally back liberal candidates. And following the theme of other Democrats around the country, he has repeatedly tried to paint Saiki as the candidate of the wealthy who supports tax breaks for the rich.

Akaka's campaign contends that it got a boost on the "fairness issue" from President Bush's weekend campaign swing here. After Bush held an exclusive black-tie Republican fund-raiser to aid Saiki's campaign, Akaka countered Tuesday with an open public rally at a high school auditorium featuring his own Washington heavy hitter, Sen. Edward M. Kennedy (D-Mass.).

Kennedy praised Akaka as one of the few senators up for reelection this year to support the controversial deficit-reduction package. Saiki voted against the measure because it raised income taxes, and she has been using her most recent television commercials to portray Akaka as an old-fashioned "tax and spend" liberal.

Saiki's break with Bush over the budget and over his veto of civil rights legislation has raised a tricky political question for her campaign -- how much to identify with a president whose popularity continues to drop. On the one hand, Saiki has presented herself as a GOP "insider" who would give Hawaii access to the White House. Bush personally persuaded Saiki to run for the Senate seat.

On the other hand, Saiki has been successful in her two campaigns for the House largely by playing down her party and stressing her independence. When Saiki was held up in Washington last weekend by the final House budget vote -- and turned down Bush's invitation to ride on Air Force One to attend her own fund-raiser -- speculation immediately began that the candidate was attempting to distance herself from the president. Saiki said she was disappointed to have missed the fund-raiser.

Akaka's camp contends that if the race is tied going into Election Day, their candidate may have the edge because of the state's old-style Democratic machine that can get out the vote. In a small state where the winner needs only 200,000 votes, Democrats can rely on several hundred phone banks, thousands of Election Day volunteers and an army of government workers.

But as one Republican official here predicted gleefully, "The bigger the turnout the better for us. Twenty-nine percent of those government workers are Japanese."