In times of crisis when the state cannot effectively address the scope and magnitude of what has happened, the governor of that state might call on the federal government for assistance. As previously identified, this might happen during natural crises. Another occasion when this might happen would be during a particularly horrific incident. For example, when there is a sudden and unexpected loss of life, such as after a terrorist attack or some other type of incident where immediate need and assistance is required. Another moment might be when the magnitude of the situation is too much for local authorities. Recently, taped conversations were made public between then President Lyndon Johnson and Chicago Mayor Richard Daley about how the governor of the state will ask for help and how this request has to be honored given the chaos at the 1968 Democratic National Convention. For the most part, a governor calls on the federal government for help when the situation is beyond local authority control.
This is most likely to happen when a state has experienced a natural disaster of some sort. For example, when Hurricane Katrina hit the Gulf Coast of the US, the governors of the various states down there asked for federal help in taking care of the effects of the storm.
States will often ask for financial help from the federal government as well. They will ask the federal government to give them more money for education, for example. However, they will not usually ask the federal government to come in and actually take over for them except in cases of disasters.