Anna Harrison was first lady as briefly as her husband, William Henry Harrison, was president -- all of a month, and she wasn't even in Washington any of that time. She was ill that winter, and eschewed the difficulties of travel from Indiana to the East Coast to attend her husband's inauguration.
According to firstladies.org, "In sending her daughter-in-law Jane Harrison in her stead, it is not clear whether Anna Harrison did so to at least ensure that there would be a female presence and companion for the new President at the Inauguration as they anticipated his greeting thousands of well-wishers for him... or to serve at all White House functions. By education and experience, Anna Harrison was well-qualified to serve as hostess herself. No primary sources indicate her intentions. She was in good health and preparing to leave by stagecoach from Ohio to Washington when a courier arrived at the Harrison farm with the shocking news that the President had died. Anna Harrison remained in Ohio since she would not have arrived in time for the funeral services and burial of her late husband in Washington, D.C. had she attempted the arduous and lengthy trip there."
Anna Harrison also has the distinction of being grandmother of a president, though she did not live to see it. The son of her son John Scott Harrison -- she and William Henry had 10 children all together -- was Benjamin Harrison, who would be elected president in 1888.