The ordinary rules of politics say they should abandon him without a moment's regret.
Base survival instincts ought to tell them that the scandals around News Corporation are a disease that may never be cured.
A by no means exhaustive list of the horrors ahead begins with Andy Coulson and Rebekah Brooks appearing at the Leveson inquiry
The non-Murdoch press will not shirk our duty to recall the fabulous social whirl that was once the "Chipping Norton Set".
We will remind you of how Brooks, Elisabeth Murdoch and Matthew Freud slapped and scratched the backs of David and Samantha Cameron at country homes, while Jeremy Clarkson flitted in and out of their parties – gambolling through the Cotswolds like a portly court fool.
MPs will then consider whether News International
and its executives misled the Commons culture, media and sport committee.
Parliament may not be much to look at now – its members whipped, its debates formulaic, its powers eroded by the European Union, judges and devolved assemblies.
But it retains its ancient privileges.
Witnesses who knowingly mislead it are guilty of contempt of Parliament, an offence that once saw miscreants faced with the threat of imprisonment.
The select committee reported that News International's instinct in its evidence to MPs "was to cover up rather than seek out wrongdoing and discipline the perpetrators".
Contempt worthy of punishment, you might think.
But as it stands, Cameron will show a true contempt for Parliament by ordering Conservatives to stop the Commons holding Murdoch's executives to account.
Tories know that News International is nothing but trouble.
On Friday, ministers begged the Leveson inquiry to allow them advance sight of Coulson and Brooks's written evidence.
If Leveson appears bad enough, imagine if criminal trials follow.
Coulson and Brooks
were once leaders of the tabloid wing of the British right's alliance between snob and mob. Politicians bowed before them.
Celebrities feared them. I doubt that they will accept their fall from power without a fight.
Coulson and Brooks never managed to create a memorable sentence when they were reporters. But as the saying goes:
"Everybody's got a book inside them."
Their account of how Cameron entwined himself with News International will be the one piece they write that will be worth reading.
Why doesn't Cameron stop Murdoch haunting him as Iraq haunted Blair? The Labour party was once as compromised as the Tories are now.
Ed Miliband proved that he was not the doormat he seemed when he stopped playing the old games and took Murdoch on.
When critics point to Labour's past record, its leaders can say with justice that they have broken with a discredited past.
Yet Tory MPs still fight to stop Labour and the Liberal Democrats saying that Rupert Murdoch is "unfit to run a public company".
Alex Salmond still tours the studios and excuses his new friends with honeyed evasions.
In private, Conservative MPs explain themselves by saying that Murdoch's commercial rivals are intent on doing him down.
They have a point. I would feel more comfortable if editors at the BBC, ITV, Channel 4 and in the anti-Murdoch press insisted that critical reports contained a declaration of interest.
Tory MPs add that the Times is a good newspaper, and not part of some satanic conspiracy, and that SkyNews is as neutral as BBC News and noticeably less biased than Channel 4 News.
They have a case there too.
But this is politics and the Conservatives were once famed for their ruthlessness.
Abandoning a man who makes the Tories look like a party in the pocket of monopolists should be as easy as shaking a stone out of a shoe.
Greed explains the survival of deference.
My colleagues on the Guardian and the Observer say we should celebrate the end of Murdoch's power. But it isn't over.
Or, rather, it isn't over yet.
News Corporation still controls Sky and owns the Times, Sunday Times and Sun.
Conservatives and Scottish Nationalists still want the loud support of the newspapers
, most notably the Sun
You can present them with the evidence that newspapers confirm their readers' prejudices rather than changing their minds.
You can point out that the internet has weakened what power the press possessed.
It makes no difference.
Most politicians prefer praise to criticism, as do most of the rest of us.
Fear is on the reverse side of that coin.
It may be that newspapers cannot fix elections but they can destroy careers.
Hugh Grant, Sienna Miller, Tom Watson and the leaders of the Liberal Democrats deserve more praise than they have received for the courage they displayed when they took the media on.
Grant was trembling in his lawyer's office before he gave evidence to Leveson.
He knew that he would have a bad press for the rest of his life, but stepped into the witness box anyway.
News International set private detectives on Watson in the hope of finding dirt that might ruin its critic.
The greatest fear is among the Conservatives.
Murdoch's decision to release emails that showed how Jeremy Hunt
's adviser was facilitating News Corporation's takeover of BskyB was a taste of what may come.
Not just Hunt, but Cameron and George Osborne were complicit in promising sweetheart deals to News Corporation.
Coulson, Brooks, James Murdoch and Rupert Murdoch know it.
What is more, the Tory leadership suspects they can prove it.
We are in the absurd position where the Conservatives dare not stop fawning over Murdoch now for fear that he will reveal how they fawned over him in the past.
Cameron could end the absurdity in a day.
He might ally with Labour and the Liberal Democrats and take the best opportunity in years to establish the new system for regulating media monopolies Britain will need as Google and the other net giants grow.
That he lacks the bravery to seize the moment tells you all you need to know about the littleness of the man.