The U.S. Supreme Court today decided Warger v. Shauers, No. 13-517:

Federal Rule of Evidence 606(b) provides that certain juror testimony regarding what occurred in a jury room is inadmissible "[d]uring an inquiry into the validity of a verdict." The question presented in this case is whether Rule 606(b) precludes a party seeking a new trial from using one juror's affidavit of what another juror said in deliberations to demonstrate the other juror's dishonesty during voir dire. We hold that it does.

This is a civil case, but the interpretation of FRE 606(b) will control in federal criminal cases as well and will be persuasive authority in states with similar rules.  The Court rejects the claim that the rule amounts to an unconstitutional denial of the right to an impartial jury but notes in one of those infamous, hedging footnotes:

3 There may be cases of juror bias so extreme that, almost by definition, the jury trial right has been abridged. If and when such a case arises, the Court can consider whether the usual safeguards are or are not sufficient to protect the integrity of the process. We need not consider the question, however, for those facts are not presented here.

The opinion is by Justice Sotomayor, unanimous.