FILE - In this April 1, 2020, file photo, Defense Secretary Mark Esper speaks about the coronavirus in the James Brady Press Briefing Room of the White House in Washington.
The president has suggested he would use all available military force, however, if state governors couldn't stop the violence.
Asked Wednesday about Esper's standing with Trump, the White House press secretary, Kayleigh McEnany, offered something less than a ringing endorsement.
He became Trumps second Pentagon chief after his first, retired Gen. Jim Mattis, resigned in December 2018 in a policy dispute.
Milley, the Joint Chiefs chairman, also has taken heat from critics for his role in managing the response to the protests.