When you think of an American Democrat or an American Republican, who springs to mind? I ask because the big American guests at each of the party conferences this year, Bill Clinton and John McCain, do not, exactly, represent the current leadership of their respective parties. They are each enigmas in their own way, each representing both the essence of their own side, and yet also, in some ways, something deeply alien to their own partisan bases.

Between them you see the complexity of America, even under this least complex president, and glimpses of its potential future.

Clinton first. I never thought I’d ever write this, but I almost feel relieved to see him on television these days.

Yes, I remind myself of everything I didn’t like about him: his dishonesty, his slickness, his callow facility with power and small-time abuse of it.

But I also remember his actual legacy. History may well judge him a moderate conservative president, whose capacity to jettison his principles at will made him a success.

He turned a huge deficit into a huge surplus; he reformed welfare; he freed up trade; he reduced the size of government; and was prudent and cautious in foreign policy even at the expense of allowing genocides in Rwanda and Bosnia and having several chances to capture Osama Bin Laden and failing.

He described himself as an Eisenhower Republican and he wasn’t entirely wrong. Yes, his mixed but not-too-shabby record was made possible by his sharing power with the Gingrich Republicans. But that too only makes me nostalgic: for the days when one-party control of both Congress and White House was impossible; and when divided government ensured that today’s massive spending, and the corruption that follows it, couldn’t occur.

But Clinton is obviously not a figure entirely of the past. His shadow looms over his party not just because of his presidency but because of his wife. Apart from Al Gore, Hillary Clinton is still the most credible candidate for her party’s nomination in 2008. But she has a huge problem apart from her polarising effect on otherwise sane people. That huge problem is her husband.

If she were to run for the presidency what would she do with him? It’s a little hard to think of him picking out new colours for the rug in the Oval Office or obsessing about place settings at state dinners. He can’t be first husband. And first adulterer isn’t yet a formal position.

The ex-president has been doing great work with his charitable endeavours, encouraging generosity from the mega-rich like Richard Branson. But as first husband, with peerless access to the president, that would also present any number of conflicts of interest.

What to do? If I were Hillary, I’d tackle this as soon as I announced my candidacy. I’d give Bill Clinton the opportunity to be secretary of state, at once removing him from domestic policy, and taking advantage of his enormous global pull. If America really did need to rally global opposition to a nuclear-armed Iran Bill Clinton might be the diplomat to do it. Or at least that would be the plan.

As for McCain his position within his own party is more awkward than Hillary Clinton’s. McCain should have won the Republican nomination in 2000. He triumphed in New Hampshire. But in retrospect the clout the religious right demonstrated in securing the South Carolina primary for George W Bush presaged much that has followed.

The ruthless politics, the smears and the preening public religiosity of the past six years all flowed from that moment. McCain, the Republican un-Bush, emerged instead as the Democrats’ favourite conservative, the media’s darling . . . and shut out of the White House.