We are exempt employees who are required to be on call for 28 straight days 24/7 x 4 time a year. This on call is not compensated for and we are required to be available ASAP upon a call, we can not go about our daily lives on our off hours. We are also responsible to cover business as usual work on the weekends due to the company refusing to provide sufficient qualified staffing.
Is the amount of hours (672) that we are required to be on call and not participate in daily family and lifestyle activities allowed, and also by not providing sufficient staffing, they are forcing us to work a full seven day work week. What are the limitations for this.

Exempt employees are paid by the week, no matter how many or how few hours they work.

Two states have limits on how many hours an employees can work. California is one (72 hours per week and I am not sure it applies to all exempt employees, if any). Maine limits overtime to 80 hours in any two consecutive work weeks, excluding executive exempt employees.

All of that applies to hours worked.

On call time is not necessarily work time, depending upon how restricted you are. For a non-exempt employee, being on call does not require additional pay for the time on call if the restrictions are not too severe.

There is no legal requirement to pay exempt employees for being on call, no matter how tight a rein the company has on the employee.