Topeka ? Gov. Kathleen Sebelius’ proposal to give thousands of jobless Kansans an extra week of unemployment benefits may not go far enough, a key legislator said Thursday.

Under the plan, the state would still offer a maximum 26 weeks of unemployment benefits. But for one year, the state would eliminate the current one-week waiting period for the first check.

Since out-of-work Kansans typically find a job within 17 weeks, the current waiting period means they receive 16 weeks of benefits. Eliminating the one-week wait means the typical unemployed Kansan would receive 17 weeks of benefits.

Officials estimate that 51,000 Kansans would receive the extra check.

Senate President Dave Kerr said Sebelius could have proposed extending benefits past the 26th week.

“I’m not sure she’s done enough, and I’m not sure it’s targeted right,” said Kerr, R-Hutchinson.

But Sebelius said the proposal would help Kansans as soon as they lost their jobs.

The waiting period is a holdover from the days when unemployment claims were processed by hand, said Acting Human Resources Secretary Jim Garner. Thirteen states have done away with such delays, while others still have the one-week wait but eventually issue an extra check.

Sebelius said the plan was drafted by the Employment Security Advisory Council, whose 12 members include representatives of both business and labor. Legislators typically defer to the council’s recommendations on unemployment issues.

The plan also calls for repealing the state’s policy of reducing the benefits of older unemployed Kansans by the amount of any Social Security payments they receive. That change would provide another $1.2 million in benefits annually to unemployed workers.

The money would come from Kansas’ $78 million share of $8 billion in federal funds given to states last year to bolster unemployment programs.

If both changes are adopted, Kansas would still have about $60 million in federal funds for unemployment programs. Keeping the money in the state’s unemployment trust fund would delay a potential increase in employers’ contributions to jobless benefits, Garner said.

Sebelius said Kansas still would be among the most aggressive states in using the federal funds to help jobless workers. Only eight have used part of their funds for benefits.

How to spend the $78 million has been a contentious issue for a year. Legislators objected to a proposal by then-Gov. Bill Graves last year to spend $4 million upgrading computers at the Department of Human Resources, and the advisory council could not settle on a plan for using the money.