Yes, the most recent occurrence of this was Hurricane Katrina. President Bush wanted the Governor of Louisiana (Kathleen Blanco) to declare a state of emergency which would activate the State's National Guard. However it was her decision to do so. However, she did within 24 hours of him requesting her to do so. The only exception is if the "situation" involves multiple states which would give the federal government jurisdiction.
Yes, the National Guard can refuse to federalize in certain circumstances, such as when the governor of a state does not consent to the federalization or when the President does not have the authority to federalize the National Guard for a specific purpose.
They refuse to assassinate the president
According the United States Constitution, the US Senate can refuse the president's appointments. It can also reject treaties that have been agreed to by the president.
This power has essentially been removed by the Budget Control Act of 1974. It meant that the president could refuse to spend money appropriated by Congress. See the related link for more information.
George Washington
refuse to sign it into law.
congress
Theodore Roosevelt was the president that didn't shoot a helpless bear
He wasn't president then - Eisenhower was. Eisenhower did intervene.
veto
He refuse to be the king.
1796