Final answer:
The major conflict between state and federal governments, eventually resolved by a dominant federal response, was centered around the issue of slavery and states' rights, culminating in the Civil War which solidified federal supremacy.
Step-by-step explanation:
The issue that created a major conflict between state and federal governments, eventually resolved by a firm federal response, was the balance of power between these two levels of government, especially regarding the institution of slavery. The ultimate confrontation occurred during the Civil War, which was triggered by the secession of southern states following the election of President Abraham Lincoln. They were concerned with the preservation of slavery, an institution they believed Lincoln would challenge.
Two crucial Supreme Court cases, McCulloch v. Maryland (1819) and Gibbons v. Odgen (1824), signaled the beginning of a shift in power towards the national government. However, it was not until the Civil War that the power dynamics were definitively altered. The Union victory solidified national supremacy by ending the right of states to secede and challenging federal laws. Furthermore, the Reconstruction Amendments, particularly the Fourteenth and Fifteenth Amendments, mandated by Congress for the reintegration of Confederate states, underscored this federal authority.
While prior to the Civil War, the necessary and proper clause and the Tenth Amendment created bases for conflict, it was the war itself that ended the debate, confirming the role of the national government as the supreme authority within the United States federal structure.