MADISON, Wis. — Last Wednesday, in the grand Beaux-Arts Capitol here, throngs of lawmakers and tourists milled around upstairs. Matt Adamczyk, the newly elected state treasurer, however, was in his basement office — alone.

Just a week earlier, there were two other employees in the office, but Mr. Adamczyk had them fired, explaining that they were a waste of taxpayer money and no longer needed. Laptops and telephones were scattered around a table, remnants from a time when the treasurer’s office was much busier.

Next on Mr. Adamczyk’s to-do list: Get rid of his own job.

In what may be the ultimate expression of many Republicans’ desire to whittle down government to the bone, Mr. Adamczyk ran for treasurer on the promise to eliminate the position during his one and only term in office.

Despite its impressive name, the Office of the State Treasurer is virtually powerless. Most of its duties have gradually been transferred to other state agencies, like the Department of Revenue. One of the treasurer’s few remaining responsibilities is to help supervise a little-known agency called the Board of Commissioners of Public Lands.