NEW YORK (CNNMoney.com) -- More than a million people could receive an additional 13 weeks of unemployment benefits under a bill approved by the House on Tuesday.

The bill extends benefits for those living in states with jobless rates higher than 8.5%. Some 27 states, plus the District of Columbia and Puerto Rico, fall into this category. The national unemployment rate hit 9.7% in August, the highest in 26 years.

The legislation now moves to the Senate. While there is support for the measure on both sides of the aisle, senators may make significant changes to it. Finance Committee Chairman Max Baucus, D-Mont., is seeking to expand the bill to give additional weeks of benefits to people in all states, not just high unemployment ones, an aide said.

Senate Republicans, meanwhile, want to look at other funding approaches, said a spokesman for Minority Leader Mitch McConnell, R-Ky.

There is no timetable for introducing the measure in the Senate, though Democratic leaders said they want to do so soon.

Under the House bill, the extended benefits would apply to an estimated 314,000 people set to exhaust their benefits by month's end and to more than a million who will stop getting checks by the end of the year. Workers in other states could qualify if their state is expected to hit an 8.5% unemployment rate soon or meets other criteria.

"Decent, hard-working Americans from North Carolina to California have been calling my office to tell me they still cannot find work after a year or more after becoming unemployed and they need some additional help to keep their heads above water," said Rep. Jim McDermott, D-Wash., when he introduced the legislation earlier this month.

To cover the benefits, employers pay state and federal unemployment taxes. This proposal would be funded by a one-year extension of an the federal tax, which has been in place for the past three decades. Also, the legislation would require that reporting on newly hired employees include a start date, which would reduce unemployment insurance overpayments.

Republicans, however, would like to look at other ways to pay for the benefits, McConnell's spokesman said.

An estimated 400,000 people are expected to lose their checks by the end of this month and 1.4 million will by the end of the year, according to the National Employment Law Project.

The advocacy group urging the Senate to expand the benefits to all states, since every one has experienced record increases in unemployment and record numbers of workers filing for and exhausting their unemployment benefits.

"It's hard to leave 23 states out of the equation," said Maurice Emsellem, the project's policy co-director.

In most states, unemployed people receive 26 weeks of state-funded benefits. Depending on where they live, they could get federally funded extensions for a total of 79 weeks.

Calls to extend benefits

Over the past year, Congress has twice voted to extend benefits. Still, pressure has been building on Capitol Hill to extend them again as the recession wears on and unemployment continues to rise. Governors of 22 states appealed to congressional leaders last week to quickly pass extended benefits.

A record 50.7% of the unemployed failed to find work within six months of receiving benefits, according to the National Employment Law Project. There are now more than six potential workers for each opening, up from 1.7 in December 2007.

Extending benefits is crucial since unemployment often continues to rise even after the economy starts to turn around, said Chad Stone, chief economist for the Center on Budget and Policy Priorities, which advocates for workers. Also, lengthening benefits helps boost the economy since the jobless usually spend their checks.

The bill is well-targeted since it would apply to more than 80% of those about to exhaust their benefits, Stone said. They will likely continue to have the hardest time finding a new job.

The locations with unemployment rates greater than 8.5% are Alabama, Arizona, California, District of Columbia, Florida, Georgia, Idaho, Illinois, Indiana, Kentucky, Maine, Massachusetts, Michigan, Mississippi, Missouri, Nevada, New Jersey, North Carolina, New York, Ohio, Oregon, Pennsylvania, Puerto Rico, Rhode Island, South Carolina, Tennessee, Washington, Wisconsin and West Virginia.