While it remains unclear how long Todd Blanche will stay in the job, whoever ends up taking over permanently will lead a department that he has shaped in his own image.
The board had been expected to vote to approve the project last month, but it was delayed after about 32,000 mostly negative comments rolled in from across the country.
President Trump has been talking about the emergency facility beneath what was once the East Wing, details of which are usually kept secret, as he tries to justify his renovation.
The House speaker first panned, then endorsed, then punted on, then pitched and now is delaying a bill to reopen the Homeland Security Department, showing his vulnerability in the face of party rifts.