Instead of extending unemployment benefits, create temporary jobs so the unemployed can earn the payments and learn new skills.
Many of these people have valuable skills and could assist local, state, or federal offices clear up backlogs such as at the Veterans Administration. The people could be utilized in non-sensitive positions since they would be temporary.
Another place they could be utilized is at the numerous state parks or national forests to assist in keeping them up.
It would not be that difficult to create a system to account for the hours worked. It would also be a great incentive to procure employment in a permanent status.