He will probably refuse, because even if he is held in contempt, the Democrat toe sucking DOJ will refuse to prosecute. However, if he refuses, the Republicans can still make life miserable for him when they reveal the 600 pages that he withheld from the grand jury.
I thought it was normal for a prosecutor to present only one side to the grand jury. It looks like some ADA accidentally called a witness who revealed Cohen to be a damned liar though. That's not good for Bragg, even from the Dem point of view. Some prosecutors were not on board with Bragg's agenda. Some quit because of the witch hunt.