Anyone who has had anything to do with Downing Street this week knows that you don't mention a man called Mark Britnell. Britnell told a conference last October that the NHS would soon be privatised and, here's the story, Britnell appeared to have been drafted in to advise Downing Street on health reform.

Britnell's heresy was reported. And reported. Despite not denying Britnell's role to the papers, by Monday Downing St was hitting the phones, imposing a DIY superinjunction on his name.

Maybe once Britnell had had a chat with Cameron's health adviser Paul Bate, they said. But he was emphatically not a trusted confidante of David Cameron who talks with such ardour about loving the NHS. Such is Cameron's determination to express his passion for the NHS that the trees of Whitehall may be pocked with its initials in a heart, carved by the prime minister himself.

So Nick Clegg must have known what he was doing on Tuesday night, telling his weekly meeting of Lib Dem MPs and peers: "People get confused when one day they hear politicians declare how much they love the NHS. And the next they hear people describing themselves as government advisers saying that reform is a huge opportunity for big profits for health care corporations."

A day later and outside the equivalent union meeting, the Tories' 1922 Committee, the Lib Dems were branded "yellow bastards". The phrase, coined by Nick Soames, has caught on with Tory MPs. This is coalition phase 3, where teamwork is junked and it is a scrabble by the two parties to take the credit for, among other things, concessions on health. But there is also something else going on: something that could be much more damaging. It's best summed up by an observation supposedly at the 1922, explaining why they were more supportive of their health secretary, Andrew Lansley, now that Nick Clegg was attacking him. The MP giggled that they believed Vince Cable would say the Tories were being "tribal".

It was a correct self-diagnosis. Tories and Labour MPs alike jeered like Jivaro headhunters at Clegg as he presented, rather well, his plans for Lords reform on Tuesday. The emboldened Tories are getting their cue from the high command that they don't have to adore the coalition anymore; Labour have always been irritated by Lib Dems but are especially so now. Labour MP John Spellar has a maxim which goes something like: "Beating up the Tories is work, beating up the Lib Dems is pleasure."

This may not be lost on the grand old man of civility Barack Obama when he comes to Westminster next week. Recently he told a friendly journalist that he had always known he was going to win a second term, it was just the media that doubted him. But then he went on to riff that the "new politics" was dead. "This town sucks," he is supposed to have said of Washington. "People suck, you guys in the media suck."

One of Clegg's friends shared this with me: "Obama says new politics is dead over there, and I think it's dead here. Right now, two of the party leaders seem to have chosen to go tribal. On both sides of the Atlantic, the new politics is dead."

And so you see the signs that the Lib Dems have begun to realise, a bit late, they may come to rely for survival on a decision by Ed Miliband. After being repeatedly very rude about the Labour leader and all things Labour, there are now olive branches being proffered.

In the debate on Lords reform, Clegg singled out Labour politicians such as Jack Straw who had tried to make progress when in government on Lords reform. That was a marked shift for Clegg. Lib Dems now wait for an indication by Miliband as to whether he is going to hug or hit.

Cameron has some soul-searching to do, too. He will shortly make a speech about his vanishing "big society'' project – it will be meant to reassure people it still remains as central to the Cameroon agenda.

This may be mostly done to placate the likes of Steve Hilton who are growing increasingly exasperated at their subtle marginalisation. The AV referendum and the Tory relative-victory in the May elections have emboldened the anti-big society faction in the Tory party (the majority).

The two elements may be linked.

David Brooks, the US columnist who writes about ideas underpinning projects such as the big society – defined as an end to individualism and the civilising effect of communities and group morals – has a section in his book about political economies not informed by principles such as the big society.

"Once politics became a contest pitting one identity group against another, it was no longer possible to compromise," he writes in The Social Animal.

"Everything became a status war between my kind of people and your kind of people. Even a small concession came to seem like moral capitulation. Those who tried to build relationships across party lines were ostracised. Among politicians, loyalty to the party overshadowed loyalty to institutions like the Senate or the House. Politics was no longer about trade-offs, it was a contest for honour and group supremacy.

"Amidst this partisan ugliness, public trust in government and political institutions collapsed."

Without the big society, Cameron is overwhelmed by this kind of philosophy, and it bleeds into his style of politics.

The coalition was supposed to reverse all this. It was pitched to voters as the new grown-up politics of consensus, which would reverse their apathy. With the drive for differentiation between the two parties that hears talk of "yellow bastards", coalition has made politics more tribal, not less.