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Listen hard in Whitehall and you will hear the sound of what Nick Clegg told me today was a "bunfight".

Ministers are squaring up for a battle over whose budget is to be cut next. A further £11bn in cuts have to be found and announced in June even though they won't be implemented for another two years.

Today the deputy prime minister insisted that the schools budget would continue to be spent on schools and not raided to limit the cuts at the Ministry of Defence, as some reports had suggested.

"Secretaries of State will take a lot of time over the next few weeks coming up with ever more exotic reasons why their budgets shouldn't be cut and other people's should be," he said.

"That's just the nature of the Whitehall bunfight that precedes a Whitehall spending round and I can't second guess the precise details, we'll announce that in June.

"But what I can tell you, that the protections for the NHS, the protections for schools, the guarantee that we'll spend 0.7% of our national wealth on the poorest people in the world through development assistance, they will remain there.

"And of course the schools budget is for schools, it is not there to run the day-to-day operations of the ministry of defence in military terms. It is there for schools, and it will always remain there, for schools."

Nick Clegg has always maintained that he only formed a coalition with the Conservatives because that was what the public voted for. Today I asked him whether he was ready to serve as Deputy Prime Minister under Ed Miliband. A hypothetical question he says ...a decision for the country.

But when he was pushed, he replied: "Absolutely. If the public say the only way in which this country can be governed in a sensible centre-ground stable way would be as a coalition, of different combinations as now, but still involving Lib Dems, I would, just as last time - the Lib Dems would just as last time - do our duty to the country, because what we care about is doing our duty to the country, to get this country through these difficult times to create a stronger economy, but to do so as fairly as possible."

It is clear that what many may see as unthinkable is - to the Lib Dem leader - simply the logical possibility of another close general election.

In the meantime, though, he appeared to fear that UKIP could push the Lib Dems into fourth place in this week's local elections.

I asked him why the new kids on the political block were beating his party in the opinion polls.

"I don't think it's surprising," he replied. "You see it in lots of European countries, where there's a lot of economical turmoil, of course it is attractive for political parties to pop up and say we don't have to take any difficult decisions. I think the more UKIP policies - rather than the lack of them - are scrutinised, the less appealing they will become."

Asked whether there was a danger the Liberal Democrats could be relegated to the fourth party of British politics behind UKIP, he added: "I don't think that will happen in the general election."