Should States Enact Rules (as the Federal Government has done) forbidding Public Employees from Striking?

President Roosevelt (1937) forbid federal employees from striking (which is still in effect today). Many states with both Republican and Democrat governors are having to cut budgets way down in order to stay afloat. This has a serious negative direct effect on state government employees teachers, safety forces, etc. Should the states also enact rules forbidding public employees striking?