In the US, there is rarely, if ever, a contract. Unless you can show that you were let go for a legally protected cause (your age, race, religion, gender, and some other things), employers can fire you without any reason at all.

The only caveat here is the differentiation between for cause and without cause, as it impacts your ability to collect unemployment insurance payments. Employers pay those insurance premiums to the government and they are based on how often people let go from that company claim the insurance payments, so a company that lets go of a lot of employees is going to pay more than one that manages to find a way to fire them for cause or get them to quit.