Can I get married in two weeks as a U.S. citizen living in Yemen?

Would I need someone ordained in the states to sign the marriage certificate or someone in Yemen? What may be some obstacles that we could encounter? My favorite day of the year has always been December 12th and I realized that would be the perfect day to get married. I would really like to make this happen but have no idea what I need to do to get started. I would appreciate any help or suggestions that you have. I wish I had more time until that date!

We are both U.S. citizens from the same state. Our visa will change to a resident visa on the 13th of December. Will that change how we would get married?