There is an equal amount of evidence that they are well pleased that it did so. For the immediate interpretation of it - heavily reinforced by Jack Cunningham, Labour's Foreign Affairs spokesman - that Mr Major was effectively suggesting a two-speed Europe in which Britian would remain in the slow lane - may not have been quite accurate. Indeeed Mr Major himself stressed in his speech last night that a 'flexible Europe' did not mean 'we must have a first division and a second division'. But it has had a strangely unifying effect on Mr Major's most Euro-sceptic critics.
The interpretation is also likely to play well with precisely that group of voters about which the Tories are most concerned in the current European election: the core supporters who are most likely to stay at home, many of them deeply suspicious of Europe and all its works.
Lord Tebbit's welcome on Wednesday night for Mr Major's speech may actually bring some of those voters out on Thursday. And that counts more at present - in elections on which Mr Major's future could still finally depend - than an adverse reaction in continental capitals.
The fact is that the 'flexible geometry' idea, at least as floated by Douglas Hurd in his speeches in Warsaw and Inverness over the past few weeks, is not quite the same as the notion to which Lord Tebbit extended his chilly embrace on Wednesday night. On the other hand it had been - before Mr Major's Ellesmere Port speech - genuinely welcomed by 'inside right' members of the Cabinet like Michael Howard as a concept that the party can unite around.
On the stump this week, Mr Hurd expanded in an interview with the Independent on what the government means by it. Mr Hurd insisted that the multi-track idea 'has been part of our thinking since Maastricht, it's part of the Prime Minister's thinking now. We think it's already happening'.
Mr Hurd reeled off a list of examples in which 'some do, others don't'. The Western European Union in which Britain plays a key role. Bosnia, in which Britain France, Spain and the Netherlands are key participants while others are not. The European Exchange Rate Mechanism where 'we don't others do'. And so on. And in answer to the question of whether Britain can withstand the pressure for further integration on issues that are matters for inter- governmental co-operation rather than EU competence, Mr Hurd cited deregulation and subsidiarity (or minimum interference, as he prefers to call it) as examples of where Britain had at first been isolated, but had then been shown to lead the way.
He argued, too, that just as Britain and France have worked closely on Bosnia, so they see eye to eye on the issue of the need to preserve a national veto. Admitting that the 'argument is not yet over' he adds, nevertheless, that the 'old-fashioned concept of the federal European state is not going to happen'. Mr Hurd cited - as an example of the importance of keeping foreign policy as a matter for inter- governmental co-operation rather than formal EU voting - a recent discussion on how far aid to the Ukraine shoud be tied to economic and politicial reform. 'It's very important that we are able to share an analysis, discuss it, go away and reflect on it and then reach a consensus.' The alternative was a Commission proposal inviting a vote - a process much more likely to create a damaging split.
Mr Hurd is braver than most of his Cabinet colleagues - including some of his more prominent fellow pro-Europeans - in saying that Europe is indeed more than simply a free-trade area or a single market. But he is also emphatic that not everything that happens in Europe has to be reflected in an EU institution that takes its decisions by majority vote on proposals made by the European Commission.
The big question is how far, if at all, his optimisim is justified about the future intentions of Britain's European partners. He points out that Chancellor Helmut Kohl has forsworn the idea of a superstate. For the moment, the debate over flexible geometry has two advantages for the Tories. First that the simplistic interpretation may help them a little on Thursday. Secondly, a bigger prize than that: it could - just conceivably - bring a measure of unity to the party on the issue that threatens to become the Corn Laws of the 1990s.