The country would sort of go back to communism...in a way, but what would happen is a certain group of people or a person would try to get everyone to follow in their lead.then, of course, there would be quite a few opposals then chaos is started....so
Either the Vatican or N. Korea will have a spy or puppet run for president, or the U.N will seize an opportunity for a 1 world government by sending a delegate over, or the previous vice president or secretary of state will run office until further notice. These are the most likely of options.
You weren't paying attention the last election! NObody ran against Obama. Obama won! Next time Noone will be running against Nobody. For sure NotMuch will get elected though. And on and on it goes.......
I'd hate to break it to you this way but this country definitely needs a president, no questions asked. Without a president, we would go to communism. Definition of communism: a system of social organization in which all economic and social activity is controlled by a totalitarian state dominated by a single and self-perpetuating political party.