You are correct, the US has very few rights for workers, at least federally. Different states have different work protection laws, California has a lot of well known work protection laws.
49 states out of 50 are what are known as "at will employment" states (Montana is the only exception). "At will" employment means that the worker or the employer can terminate employment at any time with no notice. There are some restrictions on this, for example an employer can't fire someone because of their race, gender, sexual orientation, etc. Additionally there are laws about how larger companies have to handle mass layoffs.
49 states out of 50 are what are known as "at will employment" states (Montana is the only exception). "At will" employment means that the worker or the employer can terminate employment at any time with no notice. There are some restrictions on this, for example an employer can't fire someone because of their race, gender, sexual orientation, etc. Additionally there are laws about how larger companies have to handle mass layoffs.