The Labour spin doctors Alastair Campbell and Charlie Whelan once concocted a bogus focus group report showing that Mr Clarke was the Tory with most public support - and leaked it to the BBC. At the time, the Tory Labour feared most was Michael Heseltine.
This time, Labour's fear of Mr Clarke is real. True, some Labour modernisers think David Cameron has a better grasp of the scale of the change the Tories need to make to regain power. They respect the street-fighting credentials of David Davis but would relish an election in which he offered tax cuts and Labour investment in public services.
But most Labour folk judge Mr Clarke would be a more potent threat. They suspect he would be a credible alternative prime minister and might well make the Tories a credible alternative government for the first time since 1999.
The more interesting ripples caused by his entry into the Tory leadership race have been felt by the Liberal Democrats. Senior Liberal Democrats are already thinking what has been unthinkable: if there is a hung parliament after the next election, it is possible they could forge a pact with a Clarke-led Tory party.
I know this is playing fantasy politics. Mr Clarke hasn't won yet. Mr Davis, who is deliberately keeping his powder dry, remains the favourite. Charles Kennedy's party would not get into bed with him. Even if Mr Clarke lands the Tory crown, the election might have a clear winner and all bets would be off.
In a hung parliament, Labour and the Liberal Democrats would, on the face of it, make more natural bedfellows. Gordon Brown, who would almost certainly be Labour leader, has never cuddled up to the Liberal Democrats like Tony Blair, who only dumped Paddy Ashdown because he won a landslide in 1997. But these days the Chancellor keeps his lines open to the Liberal Democrats, knowing that he may need a good relationship with them one day.
Mr Brown wants to create a "progressive consensus" and may embrace constitutional change to achieve it. So he just might offer electoral reform for Westminster and local government to keep Mr Kennedy's party on board. The Tories, despite three crushing defeats, show no signs of embracing a fairer voting system.
Yet a Con-Lib partnership if no party wins a majority is not as remote a prospect as it seems. "If Clarke were leader, I suspect we would do business," one prominent Liberal Democrat told me. Another added: "We would be reluctant to prop up a dying Labour government. That could be electoral suicide."
Of course, Mr Clarke is not going to talk about hung parliaments. His selling point to his own party is that he is the man to haul them back into power. That means seeing off the Liberal Democrat threat, which is a real one. The Con-Lib fight will be a crucial battleground at the next election, and Mr Clarke looks well placed to win back the natural Tory supporters
Mr Clarke is well aware of the common ground between his One Nation brand of Toryism and Mr Kennedy's party. As he told the Daily Mail this week: "Some of the younger [Liberal Democrat] MPs would have difficulty explaining why they weren't in a Clarke-led Conservative Party ... I regard it as a reproof to the Conservative Party that some of these people wound up as Liberal Democrats at all."
The Liberal Democrats fear Mr Clarke. But they also like him and share his views on Iraq and Europe. His strong opposition to draconian anti-terrorist laws could have been produced by Liberal Democrats' central casting.
A significant group of Liberal Democrats including David Laws, the party's pensions spokesman, who favour market-based reforms to public services, are on the same page as Mr Clarke, who was a reforming Cabinet minister.
Some Liberal Democrats even raise the intriguing if fanciful prospect of a permanent alliance with a Clarke-led Tory party, while Labour under the more tribal Mr Brown reverts to type after Mr Blair's departure.
That is surely taking fantasy politics too far. For a start, the rest of the Tory party is not going to disappear and Mr Clarke, for all his strengths, is not at its centre of gravity. Mr Brown would do some things differently but he is not going to declare war on the voters Mr Blair has wooed so effectively.
Yet a temporary agreement between the Tories and Liberal Democrats until the next election is not impossible. One senior Tory said: "It wouldn't be a coalition. But there could be an understanding like the Lib-Lab pact that sustained Jim Callaghan. If the centre-right Liberal Democrats are in the ascendancy, all things are possible."
Mr Blair was convinced by Roy Jenkins of the need to reunite Britain's two progressive parties after the Tories enjoyed power for most of the last century. It would be ironic if party politics realigned in a very different way after he departs.