Division of power had been an issue since before the Constitution was drafted. Indeed the Articles of Confederation were carefully drafted to protect the rights of the states vis a vis the General government. Obviously, that government was not workable, and the division of powers came into play again at the Constitutional convention and shortly thereafter.
The true issue governing division of power was interpretation of the Constitution. Some, such as Alexander Hamilton, preferred to construe it broadly and allow the Federal government any powers not specifically denied to it by the Constitution. Others, such as Thomas Jefferson and James Madison, argued for a strict construction with power belonging to the states unless it was expressly granted to the Federal government or denied to the states. The problem raised its ugly head several times almost immediately after the new government was formed. Jefferson and Madison argued against formation of the Bank of the United States; they believed that Congress had not given the power to the Federal government to form a bank; rather that power was reserved to the States under the 10th Amendment. It again came to the forefront with the passage of the Alien and Sedition Acts. Jefferson and Madison secured the Kentucky and Virginia resolutions which said states had the right to declare Acts of Congress unconstitutional within their respective borders. John C. Calhoun later raised the same issue in the Nullification doctrine mentioned in the answer above. Chief Justice John Marshall attempted to put the matter to rest in the case of McCulloch vs. Maryland in which he argued that any act of Congress which could legitimately be tied to the Constitution was constitutional. The Supremacy Clause of the Constitution states that the Constitution, any Federal Laws or Treaties passed pursuant thereto are the "Supreme Law of the Land," to the exclusion of any act of the States. Marshall relied on this clause in his argument; however it did not put it to rest. It is still around, with conservatives--particularly the Tea Party--arguing for a Strict interpretation of the Constitution with more power to the states; Liberals argue for a more broad construction.
There were many issues that brought the issue of federalism to the fore in the early decades of the US. Here are a few of those issues:
- Transportation. There were issues over whether the federal government should help to fund things like roads that would help create a better transportation network in the country. In addition, there were issues over steamboat transport between states. The issue here was whether the states could regulate trade with one another or if that was only the province of the federal government.
- Slavery. By the middle of the 1800s, the issue of slavery was a major one between the Southern states and the federal government. There were disagreements as to whether the federal government could prevent slavery from spreading, for example.
- Nullification. This was perhaps the biggest deal of all. There was a dispute as to whether the state governments could judge a federal law to be unconstitutional. This dispute led to threats of secession on the part of South Carolina.