Shortly before inauguration, Mr. [Jim] Mattis signaled he intended to pick Michele A. Flournoy, a hawkish Democrat who would most likely have been Hillary Clinton's defense secretary, as his chief deputy [at DoD].
The pick stunned Mr. Trump's advisers. Stephen K. Bannon, then the president's chief strategist, warned that it would infuriate longtime loyalists of the president and influential conservative senators, such as Tom Cotton or Arkansas. Ms. Flournoy, according to people with direct knowledge of the exchange, told the new secretary he would lose the fight, but Mr. Mattis, a veteran combat commander, assured her that he would win - and he prevailed, gaining Mr. Bannon's unlikely blessing.
Ultimately, Ms. Flournoy opted against taking the job...
Here is a previous Think Tank Watch piece about why Flournoy turned down the job.