Q. Is it legal to require
A. Yes, you can require a longer notice from management. But you need to be aware of some important points. First, unless that notice requirement is part of a valid employment contract, it may not be enforceable. Second, requiring notice of intent to resign could potentially jeopardize an employee's at-will status. So place your “extra-notice” policy in a contract if you want it to stick, but beware of the at-will impact.
Finally, if you have any plans to take away employees' unused vacation time if they don't provide adequate notice, check your state law first. Some states, such as California, say accrued vacation can't be forfeited.