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Change is slow, however. Mrs. Norton predicted on Mr. Colbert’s show a year ago that she would soon be a full voting member; Mr. Colbert called her a “fake congresswoman.” But momentum to give her voting powers stalled when an amendment was added in the Senate that would repeal a strict city gun-registration requirement, something Democrats did not want.

Mrs. Norton said she believes she may now have found a way around the amendment and will get the bill passed early this year.

Lifelong resident Jenica Degree, who works at a store that sells political memorabilia, isn’t convinced that having a voting congresswoman would change much. Not having one “really doesn’t bother me,” she said.