Yet to be seen. Chutkan has demonstrated that she's going to be the "find out" of "fuck around" in other aspects, but she also knows she is presiding over a uniquely historic case with potentially terminal consequences. Her Friday statement about inflammatory public comments demanding a swift trial fell short of what I would have liked, but I find her decision on the matter to be brilliantly fair, and unassailable.
Also note that the Government has not (so far as we know) made any motions in response to the defendant's weekend commentary. Based on the immediate motion for a protective order after the defendant's "I'm coming after you!" post, I might expect there to be a motion from the Government, and there's not (again, so far as we know). To me, this suggests that they know Judge Chutkan is already working on this, and does not need the Government or public pressure to be any greater than it already is. And if they know, defense knows, too.
I am hopeful, but the consequences (if any) for the defendant's weekend rants are going to be the point upon which the future of democracy turns. She has to know this, and I have to think that the reason we haven't heard anything from her yet is because she is considering very carefully what the response from the court will be.