Who administers direct democracy mechanisms at the national level?

Federal Law on Popular Referendum (March 14, 2014)

Article 3. The Congress of the Union, the Supreme Court of Justice of the Nation, the Federal Electoral Institute and the Electoral Court of the Federal Judicial Branch are responsible for the implementation of this Law, within their respective areas of competence.

For the case of the Federal Electoral Institute, its executive directions and technical units centrally are responsible for the organization and development of the popular referendum; regarding deconcentrated bodies, the councils and the corresponding local and district executive boards will be competent thereof.