The vice president who resigned to lead the fight against the 1832 tariff was:

John C Calhoun

He resigned as a result of the passage of the Tariff of Abominations. The South at that time was reliant on cheap foreign goods-the European market was over-saturated with goods and fairly stagnant, while the American market was growing and goods were scarce enought to get good prices. So, in order to protect American manufacturers, Congress passed and Jackson signed the Tariff of 1828, raising the price of foreign goods above that of the products of American manufacturers.