National security adviser Condoleezza Rice, who is frequently mentioned as a possible candidate, has told associates she is not interested in handling the diplomatic tedium and bureaucracy that comes with the job. Dark-horse candidates include centrist Democrats, such as former senator Sam Nunn, or someone with bipartisan appeal such as Sen. Richard G. Lugar (R-Ind.).
Rice wants to head the Defense Department, according to several Republicans, but Secretary Donald H. Rumsfeld is lobbying to keep his job, hoping for progress in Iraq and some success with Bush's agenda of military modernization.

President Bush meets with his Cabinet at the White House for the first time since being reelected.
(Ron Edmonds -- AP)
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Post reporter Jim VandeHei discusses the likely changes in President Bush's cabinet over the next couple of months.
The Post's Dana Milbank reviews President Bush's news conference.
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"Rumsfeld wants to restore the golden-boy glow before he leaves," said a presidential adviser who has discussed the matter with top Bush aides.
If Rice moves to the Pentagon or leaves altogether, as some suggest, there will be a heated competition for her post. Her deputy, Stephen J. Hadley, could move up. But he would face tough competition from three important players: Paul D. Wolfowitz, deputy defense secretary and architect of the attack on Iraq; Robert Blackwill, a hard-charging former ambassador to India who now handles Iraq policy at the National Security Council; and I. Lewis "Scooter" Libby, chief of staff to Vice President Cheney. Libby, at the moment, however, appears more likely to continue in his powerful role as Cheney's chief aide.
Ridge, the first secretary of the Department of Homeland Security, has indicated to friends that he wants to move on, too. Department sources said Ridge has not made any decisions except that if he were to remain for the start of Bush's second term, he would not stay for all four years. The sources said Ridge has a full schedule until the end of the year, and is likely to stay until then to avoid signaling a lack of leadership during the holiday period, which has been a time of security concern in the past couple of years.
Ridge has spent three intense years in the federal government, first as Bush's top homeland security adviser and then as head of the 170,000-employee department. Facing college tuition for two children, he also has expressed a desire to join the private sector after decades in government.
There is no clear favorite to replace Ridge, though White House officials are looking for jobs for several loyal Republicans, including Dan Coats, the U.S. ambassador to Germany, and Marc Racicot, who helped run the president's reelection campaign, officials said. Thompson is another possibility, Republicans in the government said.
Ashcroft's aides have been saying for months that the attorney general, who has spent nearly four years in the high-pressure job as the nation's chief law enforcement officer and missed nearly a month of work this year when he underwent surgery for pancreatitis, would probably leave before the start of a second Bush term. White House officials say privately that Ashcroft is almost certainly gone.
But a senior Justice Department official said yesterday that Ashcroft was reconsidering because he was "energized" by the strong GOP showing on Tuesday.
Christian groups have called the White House in recent days with messages of support for Ashcroft as a result of speculation in the news media that Ashcroft will soon depart, a Justice official said. Hundreds of calls and e-mails have come in to the department as well, he said.
One Justice official noted that heavy turnout among evangelical Christians was a crucial part of Bush's support and said the Justice Department's handling of terrorism was also a strong selling point among voters.
Danforth, a former attorney general in Missouri, is considered a top contender for the post if Ashcroft leaves. Other possible replacements include former deputy attorney general Larry D. Thompson, who would become the first African American to head the Justice Department; White House counsel Alberto R. Gonzales, who would be the first Hispanic to hold that post; and Racicot.
Treasury Secretary John W. Snow is likely to be replaced but will be given plenty of time to make a graceful exit, administration officials involved in the discussions said. Card is a possible replacement, although he is planning to stay in his job for now, friends said. One top administration official said U.S. Trade Representative Robert B. Zoellick is interested in the job but unlikely to get it.
Commerce Secretary Donald L. Evans has not said he is leaving but has sent strong signals that he plans to return to Texas, administration officials said.
Staff writers Mike Allen, Ceci Connolly, Michael Dobbs, Dan Eggen, Sara Kehaulani Goo, Al Kamen, Dafna Linzer, Christopher Lee, John Mintz and Susan Schmidt contributed to this report.