President Bush often insists he has to be the decider — ignoring Congress and the public when it comes to the tough matters on war, terrorism and torture, even deciding whether an ordinary man in Florida should be allowed to let his wife die with dignity. Apparently that burden does not apply to the functioning of one of the most vital government agencies, the Justice Department.

Americans have been waiting months for Mr. Bush to fire Attorney General Alberto Gonzales, who long ago proved that he was incompetent and more recently has proved that he can’t tell the truth. Mr. Bush refused to fire him after it was clear Mr. Gonzales lied about his role in the political purge of nine federal prosecutors. And he is still refusing to do so — even after testimony by the F.B.I. director, Robert Mueller, that suggests that Mr. Gonzales either lied to Congress about Mr. Bush’s warrantless wiretapping operation or at the very least twisted the truth so badly that it amounts to the same thing.

Mr. Gonzales has now told Congress twice that there was no dissent in the government about Mr. Bush’s decision to authorize the National Security Agency to spy on Americans’ international calls and e-mails without obtaining the legally required warrant. Mr. Mueller and James Comey, a former deputy attorney general, say that is not true. Not only was there disagreement, but they also say that they almost resigned over the dispute.

Both men say that in March 2004 — when Mr. Gonzales was still the White House counsel — the Justice Department refused to endorse a continuation of the wiretapping program because it was illegal. (Mr. Comey was running the department temporarily because Attorney General John Ashcroft had emergency surgery.) Unwilling to accept that conclusion, Vice President Dick Cheney sent Mr. Gonzales and another official to Mr. Ashcroft’s hospital room to get him to approve the wiretapping.