The 'Madonna Effect'

I posted yesterday about Madonna being called to jury duty and it reminded me of when I was called to jury duty.  No, I am not a pop star, but I got the impression that I wasn't going to be on a jury the last time I was called because I am a lawyer.  It got me thinking about whether a juror can be disqualified for cause because of the effect another juror has on them. No lawyer would think that Madonna should be excused because of her status, but what about the other jurors.  In this case, it seems that the jurors who are adoring fans may be excused for cause if they say that they could not be fair and impartial on account that Madonna is sitting right next to them. Should the court have private questioning of the jurors dealing with the 'Madonna effect'?