Despite it being in the constitution, this "legal theory" has never really been successful. Numerous states have tried to use the nullification clause and failed.
Not to say I disagree with it, or agree with it, but don't get your hopes up..
A similar one that is also rarely attempted AFAIK is Jury Nullification [1] I've heard it suggested to be used to be disqualified for jury selection but have no idea how many people have actually tried to use it. i.e. that ones states to the lawyers during jury selection that they believe in the use of invoking it Here's [2] a video about it.
I'd say the jury nullification has absolutely been successful and used many times. O.J. Simpson anyone? The man murdered two people and was found not guilty because the jurors wanted to send a message to the police. They didn't nullify based on a specific law, but it was government policy. That may have been one of the most atrocious miscarriages of justice in American jurisprudence.