A salaried employee can be non-exempt (i.e., covered by the FLSA). This might be the case with you. Without knowing what your job entails, I cannot say; but here is some help in this regard.
If you visit the Department of Labor website (www.DOL.gov), you can see definitions of what constitutes exempt and non-exempt under the FLSA. Click on "Frequently Asked Questions," which should make you feel comfortable because it means that this confusion is widespread.
If your job legitimately is exempt, it is true that you can be expected to work some holidays and/or weekends--if doing so is necessary to accomplish the fundamental job objectives.
But it sounds to me as though your employer is trying to cover two jobs by requiring you to work in excess of 40 hours all the time and now weekends and holidays, as well.
Requiring an exempt worker to work specific hours may negate the classification of the job and make it non-exempt. That is, what makes a job exempt from the FLSA is primarily the nature of the work being done and the amount of control the job incumbent has in accomplishing his/her duties. An exempt classification is bestowed to jobs that allow the workers to control their productivity and, therefore, the time devoted to completing their assignments.
Some examples of types of exempt workers are: executives, administrative employees who exercise independent judgment in carrying out their responsibilities, professionals and employees engaged in certain computer jobs or in outside sales.
If you feel that you should be re-classified and paid overtime for hours worked over 40 in a week (or 8 hours in a day, depending on in what State you work), contact the Department of Labor and report the situation. They will help you resolve it.