They didn’t actually nullify the A&S Acts. The Virginia & Kentucky Resolutions of 1798, Kentucky Resolutions of 1799, and Virginia Report of 1800 laid out the Republicans’ view of the Constitution, including the claim that in case the Federal Government adopted a policy that was unconstitutional and dangerous, the states (and these are the words of Virginia’s third resolution) “have the right, and are in duty bound, to interpose.”
What “to interpose” meant in this context remained unclear, although Virginia’s reference to the states’ doing so “within their respective limits” gave a hint. So too did the fact that Virginia in that year also finally concluded several years’ debate over whether to build a new state armory and actually did construct one in Richmond, as well as beginning to heighten training for militia units throughout the state. Some of those militia units, such as the famous Richmond “Republican Blues” cavalry unit, were forthrightly partisan.
One common error concerning the VA & KY Resolutions is to assume that they meant what Madison wanted them to mean, or later said they meant. As I show in _Virginia’s American Revolution_, ch. 4, and _James Madison and the Making of America_, however, the discussions in the Virginia House of Delegates centered on the idea that all unconstitutional federal policies were by definition “null, void, and of no force or effect” — so that removal of that phrase from the final version of the Virginia Resolutions did not negate that claim. Calling federal policies not legitimated by the Constitution’s express provisions “unconstitutional” was censure enough.