Some Tories still respond to interviewers by banging on about the single currency and which wing of the party will produce the new leader, but wiser minds are focusing on the enormity of the task ahead. In short, they believe, the new man or woman must do to the Conservative Party what Blair, and before him Neil Kinnock and John Smith, did to Labour. If they do not, the Tories could face virtual extinction.
Their position is acute. Labour was on its knees when Mrs Thatcher enjoyed her greatest triumph in 1983 (with an overall majority 35 fewer than Blair's). Recovery for Labour has taken 14 painful years. In many ways, though, the Tory condition in 1997 is even graver than Labour's in 1983. No MPs in Scotland and Wales, wiped out of many town halls, hardly any decent- sized towns and cities to run. And now, swamped at Westminster.
Worse, there are few Tory strongholds any more. Places where the party has never had to try very hard, safe in the knowledge that well-heeled voters will always support those who profess to stand for low taxation, have become marginals.
It was this, said one senior Tory MP, that made Thursday's result so shocking, and worrying. Everyone seized on the headline figures of a Labour majority of 179, and 178 Tory MPs losing their seats. But other numbers are causing Tory hearts to miss a beat.
In Hertfordshire North-East, the Tory majority had been a thumping 14,000. When the next election comes, they must defend a slender 3,000. Westmorland and Lonsdale saw the Tory margin cut from 15,000 to 4,000.
Safe Tory seats have become Tory marginals - and this is a party that traditionally has looked down on marginals. Peter Thurnham, the ex-Tory MP turned Liberal Democrat, recounts how he was told by the grandee in charge of choosing would-be MPs: "If you want one piece of advice, have nothing to do with a marginal."
This attitude, said Thurnham, runs right through the higher reaches of the party. "There is an in-built arrogance there, which says that MPs from marginals are inferior creatures."
Suddenly, even the senior ranks are made up of such failures. People who have never had to sweat, to pound the streets, to hit the phones and win over floating voters, will have to do just that come 2002.
And what most alarms senior Tories is the knowledge that their party is in no fit state to fight. For all its gloss, theirs is not a campaigning party at the local level. The new leader must not only unite the factions over Europe, but take the organisation into the 21st century. Behind the sleek facade of wealth and - before last Thursday - invincibility, the machine is falling to bits.
In many parts of the country the Conservative Party is too poor to pay a local agent's wages. Money raised by the centre to fight elections has not filtered down to the grassroots. In plenty of constituencies, the party's hard-core is a handful of people: a few councillors if it is lucky, but not enough firepower to mount a serious campaign.
While the centre at Westminster and Smith Square has gloried in power, local associations have become increasingly disillusioned, seeing headquarters as over-blown, arrogant and incompetent. An assistant to a successful Tory industrialist who is a champion of lean management said he could not believe what he found when he visited Smith Square: "It was like the head office of every company we have ever taken over. The people stuck to the old-fashioned attitude that the members were there to do their bidding, not the other way round."
But the Tories have been in retreat as a political force for years. Almost half its members are 66 or over; the average age is 62. "We have plenty of little old ladies who can stuff envelopes," said one shattered, younger activist on Friday, "but they do not like cold-calling, or knocking on doors. They do not like having doors slammed in their faces. They also have no idea about modern polling techniques. We do not have enough people who can use computers and feel comfy with information technology."
This was where Labour and the Liberal Democrats ran the Tories into the ground in the last two months. Their work-rates were higher, they had more people on the ground, their canvassing was more sophisticated, they were hungrier for success.
On Thursday, every voter in the marginal Richmond Park seat got a "good morning" notice from the Liberal Democrats. This was the last of a stream of leaflets and door-to-door visits. From the Tories in the six weeks there had been barely a whisper. Result: defeat for Jeremy Hanley, the former Tory chairman.
After 18 years in office the Tories had become complacent. The Young Conservatives, once the prop of the party, has been allowed to wither away. Once, the YCs had 500,000 members; today, there are less than 7,000. In universities, the party actively disbanded student organisations because they were seen as an embarrassment. Under Blair, Labour has boosted its membership and wooed supporters from the younger age group.
Some senior Tories accept that younger people are more likely to turn to radical politics - and as the party in power for almost two decades that was something they could not offer - but they find the way a once awesome machine has been allowed to collapse, inexcusable.
"What Blair did was to build a modern political party," said a constituency official. "We have a political party which is the greatest political organisation of the nineteenth century."
Labour and the Liberal Democrats are run firmly from the centre. But the Tory constitution still allows free rein to the local constituency associations - with alarming results.
Take Neil Hamilton. One of the running sores of the campaign was his decision not to stand down in Tatton, which is what Central Office wanted, to end the sleaze allegations and bring the campaign back to real issues. When Tatton's Tories backed Mr Hamilton, Smith Square was powerless to intervene, so sleaze never went away.
Whoever takes over as leader will have to abolish the lingering squirearchical culture. "It is like a theoretical exercise: you build a party, elect a leader, and plan a campaign to win back 200 seats," said a senior party worker. "Labour have done that; now we need to do it."
That may prove more difficult than it sounds. "What is there to fight against when our opponents have adopted most of our policies?" asked a former Smith Square campaigner.
The Tories are not entirely without hope. Blair may make mistakes. The Labour left may rear its head again. The first test will be the elections to the European Parliament in two years' time. "They are like a nation- wide by-election, offering power without responsibility," said the senior party worker. "Maybe, our comeback will have started by then." Maybe.