Holding a bitter contest while recriminations are being traded over the general election defeat could lead to a repeat of 1997, when MPs panicked and picked the man who led them to a second catastrophic defeat.
Senior Tories pleaded with Mr Hague throughout Thursday night to stay on because many shadow ministers privately hoped to delay a leadership contest, possibly until after a referendum on British membership of the euro. They calculated that a win for the Yes camp would present an ideal opportunity to rally the Tory pro and anti-Europeans behind a new leader. A No win would have ensured Mr Hague's survival.
Such a scenario ended with Mr Hague's abrupt departure on the steps of Tory central office shortly before 8am yesterday. All the potential candidates for his crown were keeping their counsel yesterday, knowing that any precipitate remarks could backfire. Behind the scenes, however, the phones were buzzing as acolytes of the runners and riders sounded out MPs to gauge the level of support for their candidates.
Michael Portillo, the shadow chancellor, who was said to be heading for Morocco yesterday, and Iain Duncan Smith, the fiercely Eurosceptic shadow defence secretary, emerged as the two early frontrunners.
Mr Portillo is best placed to become the "unity candidate" who could win support from the One Nation wing, in the wake of his recent appeals for the Tories to be more inclusive, while retaining the support of Eurosceptic right.
Mr Duncan Smith, who is regarded as a hero on the right after he turned down job offers from Mr Major, will present a formidable challenge. A family man and son of a war hero, Mr Duncan Smith is likely to be endorsed by Margaret Thatcher whose views will be a crucial element in the leadership contest.
The new rules governing the leadership, in which party members choose from the two candidates who top the ballot of Tory MPs, means that the other potential candidates cannot be discounted.
Kenneth Clarke, the pro-European former chancellor who said he would spend the weekend "reflecting" on the defeat, is unlikely to win much sup port from the overwhelmingly Eurosceptic parliamentary party. However, Mr Clarke is a popular candidate among former Tory voters, meaning that he could develop momentum if the party decides that a return to the centre ground is the only way back to office.
Michael Heseltine, the former Tory deputy prime minister, underlined this point on BBC TV yesterday: "There is only one person who has the commanding stature to appeal to the country at large and that is Ken Clarke. But this is the dilemma for the party. Are you appealing to win or are you appealing to the converted? To win you need those you have lost."
His intervention will be dismissed by Mr Clarke's rivals. Ann Widdecombe, the shadow home secretary, will be praying that she makes it through to the final two because she has been relentlessly working the "rubber chicken" circuit of Tory associations. The prospect of her name on the run-off ticket is likely to prompt a Stop Widdecombe campaign among senior Tories who believe that it would be electoral suicide to elect such a maverick to the leadership.
Moderate Tories said yesterday that the "dream ticket" would be for Mr Portillo and Mr Clarke to join forces, with one standing for the leadership and the other taking the deputy's job. "The big challenge is how we can get Ken Clarke and Michael Portillo to work together," one moderate said. "We can only make progress once we have put these divisive issues behind us."
A Portillo/Clarke ticket, supporters say, would finally bury the party's Thatcherite past, while ensuring that the party does not break up over Europe. Mr Portillo, who would be the most likely leader of the two, would have to allow Mr Clarke to join the Yes camp in a euro referendum, exacerbating Tory divisions on Europe.
A failure to bring together such prominent Tories would guarantee a bruising election contest as the pro and anti-European wings went head to head. However, Mr Portillo and Mr Clarke would agree on virtually everything else, most notably the importance of returning to the centre ground on social policy.
Mr Portillo was one of a series of shadow cabinet ministers who warned Mr Hague during the run-up to the election campaign of the dangers of concentrating his fire on saving the pound. His call, in the early hours of yesterday morning, for the party to "reflect" on the campaign was clear code for the party to return to public services - the key concern of voters in the campaign - and to sound more inclusive.
Such an approach means that Mr Portillo is likely to win the support of Francis Maude, the shadow foreign secretary, one of the party's "mods", who may flirt with the idea of standing for the leadership, though he does not have sufficient support in the parliamentary party to mount a serious campaign.
Useful links
Results
Ask Aristotle about your constituency
Talk about it
Who should lead the Tories? Should Hague have quit?
Video
See Hague make his resignation statement
Election headlines
Triumphant Blair reshuffles cabinet
Hague: I quit
Comment and analysis
George Monbiot: Labour's victory rings hollow
Austen Chamberlain: history's first Hague