Can an apartment manager charge more for a termination fee than the amount of rent that would have been owed?

IF there was some clause or term in a written lease which you had (obviously) previously agreed to, which provided for a larger termination fee, that would be enforceable. But the key is it must have been in a written lease to which you agreed.

The apartment manager may not simply, without the support of a written lease, charge you *any* termination fee at all, let alone such a large one; he would be limited to 1) seeking any previously unpaid rent; 2) seeking rent for the balance of the lease term (i.e. after you move out); and 3) seeking the cost of any repairs necessitated by damage you did to the premises.