The mandate for the census is found in article 2, section 1 of the Constitution. This seems to be the relevant bit.
Quote:
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The actual Enumeration shall be made within three Years after the first Meeting of the Congress of the United States, and within every subsequent Term of ten Years, in such Manner as they shall by Law direct.
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the 'they' who 'shall by law direct' is Congress. The President is bound to do the enumeration in the way the law passed by Congress says.
AFAIK his latest move is just face-saving, ordering the agencies to do what they are already doing as far as data-sharing goes. Haven't heard as of this minute of plans to mess with the census-taking further.