There will have to be some face saving measures for Morsi in order to avoid a civil war. No doubt there are frantic behind the scenes negotiations. The military will move cautiously. The best solution would be for Morsi to call for early elections. That would go a long way to defuse the situation. That said, the MB will not give up power easily. The MB was banned under Mubarak.
And of course, the US must have relations with the democratically elected government of Egypt. Anne Patterson is our Ambassador to Egypt, which means she is the President's personal representative. She is just following directions from the WH and NSC. I know her personally and she is a top notch diplomat whose integrity is impeccable.
I find it interesting the military decided it was necessary or even desirable to launch this coup. They must really have been under threat from the MB.