I would argue that there was only one major impact of the Nullification Controversy. Its major impact was that it helped lead to the Civil War. If I have to identify two separate impacts, I will say that it made Southerners feel less connected to the North and federal government and it made them feel as if they had less hope of staying in the Union. Both of these helped lead to the Civil War.
In the Nullification Controversy, South Carolina felt that the North had pushed a tariff law through Congress that would help the North and hurt the South. People in the state felt that this showed that the North cared nothing about the South and only wanted to look out for its own interests. When President Jackson and the federal government stopped South Carolina from nullifying the tariff (declaring it unconstitutional and not obeying it) people in the South felt that the federal government was on the side of the North and that neither the North nor the government cared about the South. This made them feel less connected to the North and to the Union and made it more likely that they would eventually try to secede.
The Nullification Controversy also made it seem as if the South had fewer options. The South felt that the North dominated the federal government and was willing to use its power to pass laws that would hurt the South. If the South could have nullified these laws, it would have been easier for them to stay in the Union because they could have blocked laws that they did not like. When they failed to nullify the tariff, it became clear that nullification was not a feasible way to protest. That meant that their only choice was to obey laws they hated or secede. This, too, made secession more likely and helped to bring about the Civil War.