THE thoughts of a second-term president turn naturally to his place in history. If re-elected, George Bush will spend the next four years in mellower mode, spurning wars and giving his attention to the folks at home. Foreign-policy zealots in the White House and the Pentagon, chastened by Iraq, will retreat to think-tanks to ponder their mistakes.
This theory of a kinder, gentler second term is surprisingly common and probably wrong. While Mr Bush may well be interested in posterity and concerned about politics at home, it is fanciful to presume, as the Economist recently declared, that the neo-conservatives are "no longer in vogue".
Without the terrible catalyst of 9/11, they may be less vocal; without the momentum for war in Iraq, they may be less active. But "the ideologues", as Tony Blair calls them in private, are unabashed and planning for four more years.
"It is inconceivable that the neo-cons would not have a prominent role in the next administration," says Jacob Heilbrunn of the Los Angeles Times, maintaining that they still make the intellectual weather in the White House.
Iran is destined to be the neo-conservatives’ initial focus if Mr Bush returns to office. Although the president said in the first debate that he would "work with the world to persuade the mullahs to abandon their nuclear ambitions", right-wing think-tanks are openly discussing the prospect of a strike on Iranian nuclear installations - not by the United States, but by Israel, with tacit or explicit US support.
Another second-term hotspot will be Russia. Neo-con intellectuals are divided. Some praise Vladimir Putin as an ally and fellow-sufferer in "the war on terror", others denounce his creeping authoritarianism, following the neo-con tenet that foreign policy must promote US-style democracy.
Iraq will be the neo-cons’ second-term albatross, although they treat it as a badge of pride. Here, too, opinion is split between those who would like to pull US troops out as soon as possible after elections can be held, and those who believe in staying for the long haul.
Donald Rumsfeld is in the first camp; William Kristol, the editor of the Murdoch-owned journal the Weekly Standard, in the second.
Yet, while UK ministers queue to apologise for faulty intelligence on Iraq, the US neo-cons take the view that the ends justified the means. They are displacing the blame for the current chaos on to Paul Bremer, former head of the coalition authority, who retaliated by saying there were not enough troops at the time of the invasion.
Mr Bush will want to keep Iraq recriminations behind the scenes and focus on politics at home. Here, neo-conservatives are harder to distinguish from regular conservatives - there is nothing especially "neo" about tax cuts, social security reform, or appointing anti-abortion judges to the Supreme Court.
The neo-conservatives’ influence does extend to the domestic agenda, but their success has been defensive rather than offensive. They have worked to promote a particular kind of US conservatism. Grover Norquist, the right-wing activist who runs Americans for Tax Reform, calls it "the limited-government, pro-free trade, immigrant-friendly Reagan coalition".
For Mr Norquist, George Bush is Ronald Reagan’s ideological heir. He has successfully beaten off the protectionist, anti-immigrant challenge, represented by Pat Buchanan, and the "American Gaullist" challenge of John McCain.
The neo-conservative network came to life under Mr Reagan, when Dick Cheney ran the Pentagon, Paul Wolfowitz was at the State Department and Donald Rumsfeld flitted in from the private sector to rehearse how government would run in a national emergency. To have protected Mr Reagan’s legacy would count as a neo-con achievement.
As Mr Heilbrunn points out, however, there was a world of difference between Mr Reagan’s two terms.
The anti-communist crusader of the first term gave way to the pro-Gorbachev treaty-signer of the second.
While such a transformation seems improbable if Mr Bush re-enters the White House, the neo-cons will be on their guard.