Judge Tanya Chutkan’s decision about whether to gag President Trump in respect of his January 6 trial — his argument that she should demur is due Monday —  has become tangled with the prospects for her future as the case’s presiding judge.

The judge, an appointee of President Obama who has handed down harsh sentences to January 6 defendants, now has two consequential decisions to make simultaneously: whether to stay on the bench — Mr. Trump wants her disqualified — and whether to mute the 45th president. Both could alter the trajectory of Special Counsel Jack Smith’s prosecution of the former president.