What is the cheapest way to travel across America?

I was really trying to find a method of traveling that involves me only having to pay $250.00 or less to get from Sioux Falls, SD to Sacramento, CA. All airplane flights, greyhound, etc are all way too expensive. I looked at AmTrak and they don't have one in Sioux Falls. I thought about couch surfers but I don't have a car to be traveling across states to stay at place to place. I'm trying to make a trip to California to see my fiance in the Air Force for her birthday on July 23rd. I'm trying to make this possible but I'm extremely broke. If someone could show me a really cheap way of traveling, that would help me enormously! Thanks :D