There’s currently a Senate-confirmed Deputy Secretary of Defense — David Norquist. Under 10 U.S.C. § 132(b), *he* is supposed to become Acting Secretary in the event of a vacancy.
Unless Trump fired him, too.
Unless Trump fired him, too.
To be clear, *if* the Federal Vacancies Reform Act allows the President to appoint someone else as Acting Secretary notwithstanding § 132(b), Miller is a valid choice (because of his Senate confirmation). But it's not at all obvious that the FVRA *does* override the DoD statute.
The last time this came up, Trump named as Acting Secretary Patrick Shanahan (who was already serving as the Deputy Secretary), which avoided the issue: https://twitter.com/steve_vladeck/status/1076901416558645250?s=20