IT IS typical of the diplomacy displayed by Hillary Clinton over her four years as secretary of state that she contrived to be as far from Washington as possible—in Perth, Australia—as speculation about her successor reached full frenzy this week. Would Barack Obama pick Susan Rice, currently America’s ambassador to the United Nations, in spite of her embarrassing misrepresentation of the recent murder of American diplomats in Libya? Or might he opt for John Kerry, the chairman of the foreign-relations committee in the Senate, in spite of the risk that the Democrats might lose the subsequent by-election for his seat? And how might that decision affect the host of other cabinet jobs thought to be up for grabs?

It is a tiring business running a big chunk of the federal government. Mrs Clinton has racked up 918,375 miles on the job visiting 112 countries. Tim Geithner, the treasury secretary, has had to cope with a state of near-perpetual crisis since he took office four years ago. Leon Panetta, the secretary of defence, is running an organisation of some 2m people and overseeing the war in Afghanistan at the age of 74. The Republican leadership of the House of Representatives is pursuing a legal battle with Eric Holder, the attorney general, who has ignored some of their subpoenas. All four have signalled, with varying degrees of clarity, that they are ready to move on—leaving vacancies in the four grandest cabinet jobs at the very least.

Mr Obama’s cabinet has had relatively little turnover so far. Only three full members have resigned: Robert Gates, his original defence secretary, who was himself a holdover from the administration of George W. Bush, and two successive commerce secretaries, Gary Locke and John Bryson—the first to become ambassador to China and the second after causing a string of traffic accidents. Some seem likely to stay on either because they visibly enjoy their jobs, like Arne Duncan, the secretary of education, or because they are in the midst of a vital task, like Kathleen Sebelius, the secretary of health and human services, who is implementing Mr Obama’s health-care reforms. Others, including Mr Geithner, are thought to have stayed until now only to avoid the disruption to their departments and the bickering with the Senate over a replacement that a resignation would probably have entailed.

The bickering will be especially vociferous if, as expected, Mr Obama nominates Jack Lew, his chief of staff, as the next secretary of the Treasury. Mr Lew managed to rub senior Republicans the wrong way during failed negotiations between the White House and Congress on a “grand bargain” to cut the deficit last year. Moreover, many had been hoping that Mr Obama would send a signal that he is serious about cutting spending and nurturing business by appointing either a successful executive (perhaps Larry Fink, the boss of Blackrock, the world’s biggest asset-management firm) or Erskine Bowles, a former investment banker and White House chief of staff who served as co-head of Mr Obama’s deficit-reduction commission in 2010. The president, however, is said to be in a fighting mood after his re-election, and generally prefers to promote loyal lieutenants of long standing, like Mr Lew.

The selection of Ms Rice as secretary of state would also spark a row. In the immediate aftermath of the Libyan attack, she was the main voice in the administration describing it, mistakenly, as an act of mob violence, rather than terrorism. Republicans have railed against this version of events as inexcusable incompetence if not wilful deceit. But after a poor showing in the elections with women and minorities, they may not want to pillory an otherwise well-qualified black woman. Mr Obama this week defiantly declared their criticism of Ms Rice “outrageous”.

The likeliest alternative to Ms Rice is Mr Kerry, who has also been spoken of as a possible secretary of defence. As a senator himself, Mr Kerry would easily win approval from the Senate for either job. But Republicans would be voting for him in part because they would have a strong candidate to fill his seat: Scott Brown, the recently defeated but nonetheless popular junior senator from Massachusetts. Another candidate to succeed Mr Panetta is Michèle Flournoy, who as undersecretary for policy was the most senior woman in the Pentagon hierarchy and would be the first female secretary of defence.

Aspiring attorneys-general are thought to include Deval Patrick, the governor of Massachusetts and a former official at the Justice Department, and Janet Napolitano, who is currently secretary of homeland security but previously served as both attorney-general and governor of Arizona. And once Mr Obama has all the grander jobs squared away, he will still need to find a third secretary of commerce.