This happened to my boyfriend while we were in Egypt. Unfortunatley, they won't let you board - you must have a passport. He is a EU citizen, and was able to get an emergency one in about two or three days. 

You should be calling the Embassy as soon as it re-opens. I just read that on holidays the US Embassies are only open for life and death situations, so that's kind of a bummer for you. It sounds like you'll need to make new travel plans. 

https://travel.state.gov/content/travel/en/international-travel/emergencies/lost-stolen-passport-abroad.html