My research shows that when presidents act against their advisers’ public positions, support for policies such as using military force declines markedly. The public views the use of force much more favorably, though, when the president acts as an adviser recommends.

If an establishment appointee such as Romney tacitly or explicitly endorses a Trump administration policy, it would probably be viewed more favorably by the public and in Congress. For Republican administrations that may be perceived as hawkish or aggressive (as Trump and Flynn’s views on the Islamic State, in particular, are), it can be helpful to get the endorsement of an adviser who is known for being more restrained. It was no accident that the Bush administration sent Powell, a known skeptic of the Iraq War, to be a public spokesman for its case. Also, if a Romney-like figure brings more of the formerly “Never Trumpers” onto his team, GOP establishment criticism could grow more muted.

On the other hand, if an establishment figure disagrees with a Trump administration policy enough to speak out against it or even resign in protest, that would signal that something is wrong. Criticism of the president from the opposition party is not nearly as newsworthy as criticism from his own party. Likewise, criticism from an administration figure such as Romney could work as a “fire alarm,” drawing the attention of Congress, the media and the generally inattentive public to the foreign-policy episode at hand. Much would depend, then, on the extent to which an establishment figure is willing to speak out.