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The Park Service had targeted the King holiday in mid-January as its deadline to complete the work, but the exact plans remained unclear until the announcement Tuesday. Now, the self-imposed deadline will not be met.

Ms. Johnson said the pending holiday put pressure on parties involved in the decision to reach a consensus, so the public would know the plans to deal with the issue.

Officials said the department’s decision to drop the quote altogether was made in consultation with the Park Service, the foundation that raised funds for the memorial and the King family.

“While our family would have of course preferred to have the entire ‘drum major’ quote used, we fully endorse and support the secretary’s proposal,” King’s sister, Christine King Farris, said.