Andrew Grice: Two manifestos become one: but how long will it hold?

"There is a coalition at the heart of the Treasury," George Osborne, the new Chancellor, told his officials yesterday. He underlined his message by welcoming his Liberal Democrat deputy, David Laws, to the Treasury building opposite St James's Park.

Mr Osborne insisted on a Liberal Democrat becoming Treasury Chief Secretary, and it was for more than presentational reasons. The Tories want to "lock in" their new partners to the inevitable public spending cuts, and so Mr Laws takes on the axeman's job earmarked for Philip Hammond if the Tories had won an overall majority. Before the election, Mr Hammond spoke of becoming a hate figure, so Mr Laws is a brave man. His appointment is a Tory insurance policy; some Tory MPs fear their party will get the pain while the Liberal Democrats pocket the gains.

The coalition's initial seven-page prospectus issued yesterday looked meaty enough, but in some ways that was the easy bit. Some tricky issues where the two parties may disagree – such as social care, prison building and fox hunting – have been put off until another day.

In other areas, the two parties have agreed to disagree – for example, on Tory plans to reward marriage in the tax system and to build more nuclear power stations. This is a sign of their different instincts – and, inevitably, of trouble ahead.

Who won? The document is a classic compromise. The Tories got the better on the economy, insisting on £6bn of public spending cuts in the current financial year. This is a significant U-turn by the Liberal Democrats, who sided with Labour in the election campaign by warning that immediate cuts could kill the recovery. Yesterday they argued that the most recent economic data was more optimistic. As they say, a week is a long time ...

The decision to boost health spending every year is a Tory win as the Liberal Democrats argued that there should be no "no-go areas" on cuts. It will put even more pressure on other departments during a government-wide spending review that takes place in the autumn – the biggest test of the coalition's resilience and one which could make or break it.

The Tories have shelved their plans to raise the threshold for inheritance tax to £1m, which has already provoked some grumbling among their right-wing MPs. Even if the Tories were governing alone, Mr Cameron's internal critics were going to demand he listen to them more after an election campaign which is coming under fire. Now they fear he will talk to his new Liberal Democrat friends and they will not get a look-in.

There is plenty in the policy agreement for the Liberal Democrats to celebrate. Their brief flirtation with a Lib-Lab pact on Monday bounced the Tories into promising a referendum on the alternative vote for Commons elections. The Tories favoured a mainly elected House of Lords, but showed little intention of doing anything about it. Some Tories described it as a "priority for a third term" but now it is high on the agenda. However, one problem remains: how to get the turkeys on the Lords benches to vote for Christmas.

All the same, the Liberal Democrats have given ground on immigration, dumping their plan for an earned amnesty and swallowing the Tory proposal for a cap on the number of immigrants coming from outside the European Union.

The EU is perhaps the area on which the two parties disagree most fundamentally. The Tories have quietly dropped their commitment to repatriating powers over employment laws from Brussels, which will anger their Eurosceptic MPs when the penny drops.

The differences are not just among backbenchers. Mr Cameron's instincts are those of a sceptic, while Mr Clegg, a former MEP and European Commission official, described the Tories' chosen bedfellows in the European Parliament as "nutters, homophobes and anti-Semites" in one of the leaders' televised debates. It now looks like a very odd alliance abroad when the Tories have joined forces with the pro-European Liberal Democrats at home.

The Dave and Nick Show was impressive yesterday but it will be very hard to keep it on the road.