President Joe Biden. Holder said he believes that if a nominee is selected by May, the administration should have time to get the new director confirmed by August. If that timeline slips, however, the Mueller term would end September 4, one week before the 10th anniversary of the 9/11 terrorist attacks on the World Trade Center and the Pentagon. Mueller has often remarked that he barely had a chance to find his desk before the 9/11 attacks occurred, and his entire decade was dominated by the fight against al Qaeda and its scattered supporters at home and abroad. CNN's Barbara Starr, Joe Sterling, Terry Frieden, Tom Cohen, John King and Chris Lawrence contributed to this report.