Turn away from the mob. Ignore the angry brigade. Let their spittle run down the walls. This is the moment for the coalition to rise above the yells of the left. The government is about to be tested to what it must not allow to be its destruction. If hollow outrage is all Labour cares to offer, then reason and calm explanation must be the coalition's answer. Outrage fails in the end. It poisons rationality, it repels the moderate, it frightens the balanced. It lures zealots into a world where everyone inside thinks the same way and no one outside wants to enter. It is where Labour is going now.

The coalition mustn't follow. Its members must steel themselves for abuse. It is tempting, of course, when you are sniped at, to snipe back. David Miliband, who has taken to Twitter like a duck to quacking, is spending his days typing out edgy little digs at the coalition, particularly the Lib Dem part of it, puffed up by righteous indignation. But a political movement cannot be sustained by resentment. Rage against the machine is an emotion, not a policy.

The Liberal Democrats need to be reminded of this now, as they endure Labour's scorn. The party is unaccustomed to provoking reactions. Some MPs are wobbling. Many are worried about the VAT rise – forgetting that not long ago they believed Labour's VAT cut would have no economic effect. Lots will be worried about Danny Alexander's search for theoretical 40% cuts. They are alarmed by jeers from a party that has no alternative economic policy.

Nick Clegg is under serious internal pressure. His understandable response has been to promote the things from the coalition that Lib Dems like. Last week we got his freedom campaign, and on Tuesday we get more detail on the alternative vote referendum. All this is fine. But AV – whose impact either way it suits everyone to exaggerate – will prove peripheral beside the budget. The coalition cannot afford liberal political reform to look like a trade-off for Tory economics. That is Labour's line. Lib Dems mustn't fall for it.

So far they haven't, quite. The budget went down surprisingly well: voters agreed with George Osborne's description of it as unavoidable. The next battle is for the spending review this autumn to be seen as fair. Some will point to the unpicking of the budget measures by the Institute for Fiscal Studies as evidence – though taken as a whole, these stand up. They'll point to the scale of cuts too. But fairness is not another term for precise financial redistribution. Indeed, a heavily redistributive budget would be seen by many as unfair.

Instead, the key to fairness is inclusivity – and this is where the coalition must direct its efforts. There must be no sense that one group is exploiting others: the rich the poor, or the poor (through welfare) everyone else. Or Conservatives the Lib Dems, of course.

You don't have to agree with the Daily Mail to understand that some people who get incapacity benefit don't deserve it, and some who could work don't; or that housing benefit has become a racket paying millions to private landlords. Labour cannot be allowed to get away with the idea that it stands as the defender of an outraged majority, victims of an ideologically extreme government.

The left is beginning to smell like sour yoghurt, a long moan against the world as it is and how the last government left it. The problem is not that Labour is heading towards interesting ideological isolation. The varied shades from pale pink to light magenta in which its serious candidates are painting themselves are not socialism. The problem is that the party is being bundled up in all sorts of shallow resentments and is assuming that the public will share this negativity.

UK politics is often characterised as a contest for the centre ground, but that misdescribes the nature of the quest. Centrism implies banality, but I don't think voters want their governments to be mundane. There is a willingness to endorse radical action if it is explained and if it looks practicable. It worked for the left under Attlee and Blair; it worked for the right under Thatcher; and it is working – so far – for this government.

That a large number of people oppose what you are doing, very strongly, can become a strength, so long as they are seen to be opposing something rooted in a kind of imperative. Eight years ago almost half a million people marched through London with the aim of blocking the hunting ban – and to their dismay, the public took the government's side. The miners' strike, the Iraq war – examples are legion. Half a million people and more will probably be marching against the budget cuts soon, and will feel just as strongly that their solidarity brings invincibility. They may be proved wrong.

Keep calm and carry on has become a cliche, but it is good advice for a government. Stay pragmatic and keep explaining, firmly, in moderate language and with courtesy. The left will howl at budget cuts that their own economic legacy makes necessary, just as the right will howl against political reform. That doesn't mean these things won't get through. The nosiest causes often fail.

There are 110 days until the spending review is published. That is not long to win people over to an understanding that the new government will be attempting a fair distribution of an unavoidable shock. But unless that case is made, the coalition endeavour cannot last.