Yes, they are called NEOs. Noncombatant Evacuation Operations.
I participated in several of these while I was in the military.
They are covered in detail in Joint Publication JP 3-68.
https://www.fas.org/irp/doddir/dod/jp3-68.pdf
NEOs are complex and touchy operations. They are paid for by the State Department, and DOS has a lot of say in how the operation is actually run. As is typical, however, the State Dept lacks the resources, manpower, security, logistics, lethality, and ability to pull these operations off. The military takes this role, however, the DoD depends upon the State Dept to clear all diplomatic hurdles, to help inform the populace of American or those holding American passports to the information regarding evacuation, and the processing of those holding passports. In some cases, we evacuation people who hold no passports whatsoever - we allow the whole "clan" into the US. This has happened in Lebanon, Haiti, and other cases I can think of.
I think Obama is a terrible President, an immoral man, and corrupt. However, there is nothing unusual with sending amphibious ships to an expanding war zone to prepare to evacuation Americans.