We have just had a very insular general election campaign, but the mood at Westminster is now determined by news from foreign capitals. There was a flurry of excitement last Wednesday when the German finance minister, Wolfgang Schaüble, suggested linking the British renegotiation to eurozone reform. It led to much talk of a European ‘Grand Bargain’, with Germany and the northern European countries given greater supervision of eurozone finances, the French and the southern Europeans given an explicit, written commitment to ‘solidarity’ within the currency union, and the British offered single-market protections, an opt-out from ‘ever closer union’ and the welfare changes it wants.

If this deal could be secured, a major Tory split over Europe would be averted. In these circumstances, 80 per cent of Tory MPs would back staying in, according to one experienced Eurosceptic campaigner.

But the weekend ended on a very different note. The French press reported that François Hollande and Angela Merkel had agreed a deal on eurozone integration which did not involve treaty change, removing Britain’s negotiating leverage. Cue much Tory grumbling about how treaty change, or at least a commitment to it, was vital to the success of the renegotiation.

In truth, things were not as good for Cameron and the renegotiation as they appeared on Wednesday, nor as bad as they looked on Monday. Over the next few months, the political class will tend to respond to every pronouncement from a European leader in the same herd-like manner that it did to opinion polls during the election campaign.

No. 10 is braced for such over-reactions. It is why Cameron has said that there’ll ‘be ups and downs — you’ll hear one day this is possible, the next day something else is impossible’. However, through this fog, his limited strategy for the renegotiation is becoming clearer. As one Cabinet minister explained, they ‘want to move it fast’ and have decided to ‘focus on three or four big things and make a really big push on them’.

The new Cabinet committee that Cameron has set up to deal with the referendum indicates the areas in which the government is seeking concessions. As well as the holders of the great offices of state, it includes policy chief Oliver Letwin, Chief Whip Mark Harper and the Europe minister David Lidington. What’s most revealing is the other two departmental secretaries of state invited, Iain Duncan Smith and Sajid Javid. The presence of the Welfare and Business Secretaries indicates that the main emphasis of the renegotiation will be on changes to EU citizens’ access to tax credits and the British welfare system, and deregulation and single-market protections for countries such as Britain which will never join the euro.

Tory insiders suggest that Duncan Smith and Javid, two of the Cabinet’s most open Eurosceptics, have been put on the committee to bind them into the government’s strategy. Having served on it, it will be harder for them to resign over the final deal.

There is a danger for Cameron in trying to crack on too quickly. As party grandees are warning privately, if he rushes the renegotiation he will irritate those in his party who don’t want to leave the EU but do want substantial change to Britain’s terms of membership. This could sour relations with the parliamentary party and make governing with a majority of 12 almost impossible.

For the moment, Cameron has momentum and events on his side. Cabinet ministers who, when the referendum was an abstraction, used to talk about resigning to vote No, strike a different tone now the vote is happening. This is partly because no one wants to align themselves with Nigel Farage. Optimistic free traders don’t want to join forces with a man who has campaigned in — to use the words of the Ukip leader’s colleague Patrick O’Flynn—a ‘snarling, thin-skinned, aggressive’ manner. Indeed, if Brussels was trying to invent the British Out campaign, it would probably come up with something similar to what Ukip became during the general election campaign.

But there is also political calculation behind this change of heart. At the moment, the chances of No winning look small. ‘Euroscepticism is scattered to the four winds,’ laments one Tory veteran of the cause. He is not alone in his pessimism. Several of those closely involved in the successful campaign against the euro predict that No will do worse this time than it did in the previous referendum in 1975, when it garnered less than a third of the vote.

However, there are two events that could change the debate. The first is the Labour leadership contest. If Andy Burnham wins, he’ll make a lot of noise about the need for renegotiation to deal with European immigrants supposedly undercutting wages of British workers. He told the Observer that ‘if Cameron doesn’t deliver legislative change in terms of abuse of the rules of free movement by agencies and the effect on people with jobs here, it won’t be good enough. It really won’t be good enough.’ Under pressure from Labour, Cameron may feel obliged to go further than he otherwise would on free movement and benefits access. Burnham’s comments are a reminder of how difficult it will be hold together a pro-European coalition that is trying to include multinationals and the trade unions.

The second is some external event, the most obvious possibility being a Greek default. The Athens government has admitted that it doesn’t have the money to pay the IMF next month. Combine this with the almost total lack of goodwill between the Syriza administration and Greece’s creditors and you can see how a default could happen. The effects on the EU would be dramatic and unpredictable. In Britain, there would almost certainly be demands to take advantage of the moment to radically alter the UK’s relationship with the EU.

For the moment, the authority that his Commons majority has given Cameron has enabled him to get the renegotiation off to a smoother start than expected. The hard part will come when he has to move beyond talking, to setting out what will change. It is then that he will need all the authority he can muster to keep his party from splitting.