If Hatch does get the nod from the White House, Shurtleff said the senator would be the right kind of person to lead the department. He said Hatch is "highly respected" by Democrats, which could make confirmation smoother.

"I would certainly support Orrin in whatever he does," Shurtleff said.

He said whoever has to take over the Justice Department will have his or her "hands full" in trying to regain credibility and boost morale of its employees.

Outside the Justice Department's main building, one member of the protest group Code Pink played a tambourine while the other sang "hey hey hey, goodbye" into a megaphone at cars going down Constitution Avenue. Code Pink members, known for showing up at congressional hearings dressed in pink police officer uniforms, have repeatedly carried banners asking Gonzales to resign. A poster showed a list with check marks next to "Libby," for Lewis "Scooter" Libby, Vice President Dick Cheney's former chief of staff who was convicted of lying and obstructing investigation in a CIA leak case; "Rove," for Karl Rove, Bush's deputy chief of staff, who announced his resignation two weeks ago; and "Gonzo" for the attorney general; with empty boxes next to Bush and Cheney.

Democrats — and some Republicans — have called for Gonzales' resignation for months because of his involvement, or lack thereof, in the Justice Department's firing of eight U.S. attorneys and the administration's policies on warrant-less wiretapping.

But Gonzales made no mention of those issues at a two-minute press conference Monday morning. Instead, he said leading the Justice Department has been one of his "greatest privileges" and that he has "lived the American dream."

"Even my worst days as attorney general have been better than my father's best days," Gonzales said.

The Senate and House Judiciary Committees have been conducting investigations into whether the administration unfairly fired U.S. attorneys based on political motives after conflicting stories came out as to why they were asked to resign.

Kyle Sampson, a Utah native who had served as Gonzales' chief of staff, resigned in March and took responsibility for the controversy that erupted over the firings before the Senate Judiciary Committee. Sampson had maintained the list of attorneys under consideration to be fired, but Gonzales said he signed off on the final decision.