When a jury of twelve can overrule SCOTUS on a case by case basis, if they disagree with the SCOTUS' ruling, then basically the SCOTUS has no influence. Only in bringing the cases before a jury are they effective. Outcomes of cases can be decided by 12 who may disagree with the SCOTUS and rule in favor of the defendant. Most jurors don't know that.
Juries can not overrule the Supreme Court. I have no clue where you're getting this concept from.
Juries have the ability to vote not guilty if enforcing the law would go against their conscience, such as when they think the law is unconstitutional. Jury refusal to apply a law (jury nullification) does not create legal precedent, and thus does not overrule the Supreme Court, or any other court for that matter.
Jury nullification is moreso used to express political dissent over a law. The jury's refusal to find a person guilty can still be appealed, and thus the judicial branch still has control over interpreting laws, applying laws, and creating legal precedent.