The Kentucky Resolution, written in 1798, was Jefferson's response to the Alien and Sedition Acts. Short version was: he wasn't a fan.

This was the kind of thing he could oppose both on principle, as it violated his notion of state and local governments holding power over a weaker federal branch, and practically, as it was targeted specifically to hurt the Democratic-Republicans.

The resolution makes the argument that the states can declare a law unconstitutional. You might notice that this is contrary to what we do now: let the Supreme Court decide. This is because that concept—judicial review—wouldn't be created until 1803 with the case of Marbury v. Madison.

The justification for this idea can be found in the Bill of Rights. The 10th Amendment states that any rights not given to the Federal government are retained by the states. Since the Federal government wasn't given the power to determine what was constitutional, then it stands to reason that the states would have it.

Furthermore, the Kentucky Resolution took opposition to another level. Say what you will about Jefferson, but the man never did anything by half measures. He introduced the concept of "nullification," which really sounds like something Ronan the Accuser would do to his enemies.

Nullification, in theory, allows a state to declare a law invalid if they think it's unconstitutional. It's really should be called the Nuh-Uh Principle, but we don't get to name things. It has never been tested in federal court, and in all likelihood would be struck down.

The concept of nullification, introduced here, is one of the foremost legal justifications for the Civil War. It has been invoked several times over the years, but never successfully. Think of it as a B-side to Jefferson's otherwise sterling career.