John Tyler was not mourned in DC because he had gone with the South. "His Accidency" was a member of the Confederate congress but died before he could reach Richmond to take his seat.
Useless trivia: Tyler's nephew, Truman Tyler, had a daughter named Grace Harrison Tyler. She in turn was the mother of Truman Dorsey, a failed dry goods store owner who left D.C. for Columbia, SC; fled to Wilmington, NC from Sherman's advance; and died on the SS General Lyon along with his wife, seven children and a colored servant.