Daniel Webster argued that state governments do not have the constitutional right to nullify federal laws.
The Nullification Crisis of 1832 occured during Andrew Jackson's presidency. In this case, the state of South Carolina was trying to nullify (void) the Tariff of "Abominations" (also known as the Tariff of 1828). South Carolinians hated this tariff because it made foreign nations less likely to trade with America, as they would be forced to pay an additional tax.
This is when South Carolina politicians (like John Calhoun) argued that the state could not follow any law that the state deemed unconstitutional. However, Daniel Webster argues in the excerpt that there is no legal precedent and nothing in the constitution that gives states this power. This showed Webster's support of Andrew Jackson and a federal government which was stronger than individual state governments.