For the most part, these efforts have come about because both levels of government want to have more power and neither level of government particularly wants to pay for the things that it does. So the levels try to take more power while simultaneously trying to push the costs on to the other level of government.
For example, Pres. Bush wanted the federal government to have a great deal more power over education. This is why he pushed Congress to pass the No Child Left Behind law instead of leaving it to the states to pass such laws. This is a case of one level trying to take more power.
At the same time, you have the states and the federal government fighting over who should have to pay how much of the costs of things like Medicare. In this case, both sides are trying to get the other to pay more.
So money and power are the main reasons why the two sides have been trying to shift power from side to side.