Yes, exactly.
In many states, US employers can terminate an employee at any time, for (almost) any reason, or for no reason at all. It's often called "At-will employment" - http://en.wikipedia.org/wiki/At-will_employment
Note that while it technically works both ways, realistically it only works to the employers benefit. The employer is allowed to fire any employee at any time, for no reason, with no recourse.
But it's considered highly inappropriate for an employee to quit without offering an employer at least two weeks notice (unless the employer has committed some sort of major misconduct, committed a crime, ceased payroll, etc).