A coalition between the Liberal Democrats and a Labour Party led by Gordon Brown would have already broken down. Brown is simply too much of a paranoid personality to co-operate with anyone who isn't a crony and a toady. He lives in a zero-sum world:
Your gain is my loss (and this provokes fury)
My gain is your loss (and this is a source of immense, if insecure, satisfaction)
Divorce courts may be made to favour paranoid politics; successfully functioning government becomes impossible under paranoid leadership.
Zero-sum gaming is not the only hallmark of paranoid personality. Brown failed because, like all paranoids, he had no (empathic) sense of the world around him. He could never sense how other people were feeling, guess what they were thinking, figure out which way the wind was blowing. Other people had to tell him,in the same way that paranoid dictators rely on their secret police. In this, he differed fundamentally from Tony Blair, who is without paranoia.
Having to have things explained to you, just because on your own you simply don't get it, provokes its own insecurity: how come these people know things that I don't? Do they really know them? Are they trying to misinform me? Are they PLOTTING?
Hence the short life of secret police chiefs under Stalin.
Hence also the drive to create distrust among those around you, to make it impossible for other people to plot against you because you have sown mutual suspicion among them. The best way to stop people ganging up on you is to make them so suspicious of each other that they can't form a gang.
David Cameron seems without paranoia, as does Nick Clegg - for all that he is persecuted.
The paranoids among the political class can't believe that it might be possible to co-operate. They think the Coalition must be a Plot.