The real issue during the Nullification Crisis of 1832 is the question of who is the final arbiter of power: the Federal government or the states? This issue called into question the real meaning of the American federal system of government. Congress intended for South Carolina to pay a tariff on manufactured goods imported into the United States. South Carolina, led by Vice President John C. Calhoun, who even resigned his position in protest, issued an Ordinance of Nullification, declaring that the offending federal law was null and void. President Jackson threatened to send federal troops to enforce the tariff. Congress concurred by passing the Force Bill of 1833. Congress and the President were intent on enforcing the Supremacy Clause of Article VI of the Constitution, which places federal law over state law. These issues would be the basis for the South's secession from the Union and the advent of the Civil War.
To me, there is really only one constitutional issue here -- who has the right or the power to decide what laws of the federal government are or are not constitutional?
In the Nullification Crisis, South Carolina was claiming that the states have the right to decide what laws are or are not constitutional. If the states have this right, then they have the right to decide which laws they will or will not follow.
The Constitution is not in any way clear on who gets to decide on constitutionality. However, since the Marbury case in 1803, it has been seen as the right of the Supreme Court to make this call.
But this is what was at stake in the Nullification Crisis (constitutionally) -- who gets to decide what is constitutional and what is not?