It's unlikely the current White House would try to enact new regulations via executive order, especially with Heller and McDonald being the 800lb gorillas in the living room. Doing so would trigger a court challenge that would not only overturn the ordinance in question, it would set further limits on what could be done with such orders.
Are we so sure that the current White House cares about future limits?
NRA Chief Range Safety Officer, Home Firearms Safety, Pistol and Rifle Instructor
"There are three classes of people: those who see, those who see when they are shown, those who do not see."
Leonardo da Vinci