How do we know? Party managers have been making heroic efforts to paper over the crack, insisting there is an ``agreed policy'' of neutrality on the single currency.
The trouble is, neither the Prime Minister nor Chancellor seem much interested in colluding with the official line of the administration they lead.
Mr Clarke, describing a policy of late entry into monetary union as ``pathetic'' was indulging in a wholly deliberate provocation - ``just baring his backside and daring everyone to kick it'', as a Tory official charmlessly put it.
Yesterday, it earned him one of the most vicious kickings that a senior Tory minister has had from the Tory press in modern times. It came in particular from the Murdoch empire, which both Mr Major and Tony Blair are so nervous of. The Sun said he should go or be sacked: ``Don't kid yourself that anyone would miss you, Ken . . . Clarke must be stamped on.'' Using notably similar language, The Times said he was dishonourable and brutally concluded: ``He would be less missed than he likes to think and little mourned.''
Given that Clarke is a chancellor with a rising economic reputation, whose pre-election Budget matters hugely to the Tories and who is speaking out bravely in what he believes is Britain's national interest, this is extraordinary stuff. A political lynch mob of compulsive disloyalists are now howling against the Chancellor for treachery - the treachery of arguing his case rather more moderately than they do theirs.
Most are not fit to tie the laces of his notoriously unhygienic suede shoes; and among the politicians in the lynch mob, there isn't one big enough to fill them.
What is Mr Major's attitude to all this? His message of support yesterday, after a junior minister openly attacked the Chancellor (put up to it, we hear), was cold and terse. Deliberately so, surely: Major's people have been briefing in ever-stronger terms about how angry he is with Clarke, and how strongly he personally opposes the single currency.
In this way, Major has been using the parliamentary lobby to send desperate semaphore signals to Clarke's bitterest critics.
The loss of Clarke would cause serious Budget problems, and perhaps market ones too: other ministers would go. Major, however, is continuing to push. After all, the Chancellor was teetering on the edge of resignation in April, and didn't go then.
Leftish Tories now fear a carefully planned ambush at the Conservative conference, when candidates in marginal seats will stride to the rostrum begging Mr Major to help them win in the spring by declaring himself personally against monetary union.
If Major ``let slip'' his own view, he would change the Government's policy: on such matters no prime minister speaks ``in a personal capacity''. That would panic many senior people in the City, who need the option of joining left genuinely open.
The clearing banks are among the businesses most affected and we should expect to see a few more names breaking silence soon, including the chief executive of Barclays, Martin Taylor.
So holding the line until May is the first purpose of the Clarkeites. But if the Tories lose the election, Clarke might still be in a pivotal position, not as a Tory leader, but as a factional leader in the new Parliament. Why? Because a Portillo or Redwood-led Tory opposition would lose the pro-European Tories. One said this week: ``I don't think anyone has ever behaved as disloyally as Redwood . . . a lot of us won't forgive him and we won't serve under him.''
As Prime Minister, Tony Blair would face just the same dilemmas and would have, no doubt, rebels on his benches. So pro-EMU Tory MPs could find themselves mattering to Britain's future in Europe, if not to the future of the Conservative Party itself.
These are deep waters. But as the anti-Brussels Tories scent victory, feeling themselves close to hounding Clarke out of politics, they should exercise a little modesty. He's a brave and tough man. It won't be as easy as that.