What is federalism? What is the continuous discussion/argument over state power verses federal power? Is there a point of apparent contradiction...

Federalism is a form of government that unites entities, such as states, cities, and counties, under one federal government. At the same time, each state and local government maintains its own separate power. In other words, the U.S. Constitution establishes a federal government in which power is shared by the federal, state, and local governments. Article 1, Section 8 of the U.S. Constitution establishes the powers of the federal government by laying out the legal rights of Congress. Article VI, clause 2, called the Supremacy Clause establishes the "supremacy of the federal government," while also granting limited rights to the states.

While the early founding fathers, such as James Madison and Thomas Jefferson, supported federalism, the early politicians debated the role of the federal government. Some, such as Judge Joseph Jones, believed in drawing clear distinctions between state and federal jurisdictions. Other much stronger anti-federalists believed that national centralized agencies should not be created at all in order to avoid any conflicts concerning "which level of government was more suited to handle a particular task" ("Federalism," American History: Oxford Research Encyclopedias).

Federalists and anti-federalists especially clashed over questions of trade and infrastructure. For example, the South opposed Congress's enactment of the Tariff of 1828 since the tariff harmed Southern trade; therefore, Vice President John C. Calhoun asserted that the Constitution granted states the right to interpret and nullify federal law in order to re-establish balance between the federal and state governments. His assertion led to South Carolina establishing a convention when the Tariff of 1832 was later enacted; "the convention passed an ordinance of nullification stating that the tariffs were 'unauthorized by the Constitution' and where therefore 'null, void, and no law, nor binding upon this State, its officers or citizens'" ("Federalism"). Similarly, federalists and anti-federalists bickered over which government--state or federal--had the right to pay for the development of infrastructure such as building roads and canals.