When might a governor call on the federal government for help?

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.