The actions the U.S. Department of State can take will depend on the nature of the crisis. Often they just issue a warning about areas of unrest, how and where to seek help, and other useful advice. In more serious situations, they may recommend that U.S. citizens leave the foreign country, and, if commercial transportation is not available, provide departure assistance, as resources permit.
In extreme situations, where local infrastructure is damaged or severely compromised, they may work with the host government, other countries, and other U.S. government agencies to arrange transportation for U.S. citizens seeking to depart. Military options are only used as a last resort. You should not expect the U.S. military to assist you when there is a Travel Warning advising you to leave a country.