WASHINGTON — The House voted overwhelmingly last night to approve a $1.4 billion stop-gap extension of jobless benefits, but some states are beginning to seek longer-term solutions to an unemployment problem that is expected to remain serious for the rest of the year and may grow worse next year.

Hawai'i Democrat Mazie Hirono was among those who voted in favor of the bill, which passed 331-83. Hawai'i Rep. Neil Abercrombie, also a Democrat, did not vote.

The extension, covering an additional 13 weeks, will maintain payments for more than 1 million workers in 29 hard-hit states whose benefits are set to expire before the end of the year. The extension does not apply to Hawai'i. Unemployment payments for more than 300,000 people will end this month alone.

The extension would apply to about 75 percent of all unemployed workers in the United States, including those in California, New York, Florida, Illinois, Pennsylvania, Michigan and Ohio.

The measure, which the Senate is expected to approve shortly, would take effect as soon as it is signed into law. It would be paid for by deferring a scheduled reduction in unemployment insurance tax paid by employers.

But with the nation's jobless rate, currently at 9.7 percent, projected to climb to double digits well into next year, researchers say that as many as 2.5 million jobless workers will exhaust benefits by next summer — sharply increasing the cost of further extensions.