Aditya Bamzai of Virginia argues that he could here. Excerpt:
[The] premise [that the president has to let the litigation runs its course] appears to rest on two mistaken assumptions: (1) that the President cannot exercise his removal authority absent an Article III judgment authorizing such removal, especially when a pending case may address the very same legal question; and (2) that the CFPB Director could resist a presidential order to vacate his office. Neither assumption is correct. If the Executive Branch determines that the statute restricting the CFPB Director’s removal is unconstitutional, the President can remove Mr. Cordray before the D.C. Circuit resolves the appeal and before any judgment becomes final.
First, the President has the authority to remove the CFPB Director absent a court decision and, therefore, before the PHH litigation runs its course. This authority follows logically from the principle that the Executive Branch may assess the constitutionality of a statute, and then act on its assessment without preexisting judicial imprimatur. * * *
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Second, in prior scenarios where the President has exercised the removal power, the officer has been unable to resist the order, but rather vacated his office and then challenged the legality of the removal through a personal lawsuit. * * *