So how should he have gone about this? Note that he wanted to do so democratically and by consent.
The natural way to do so would be to ask the 1922 Committee to propose a ballot of their backbench members, to invite the frontbench too. Cameron could have sought to powerfully persuade his MPs of the merits of the case, putting his authority as party leader and new prime minister on the line.
The reason Tory MPs have particular reason to be angry about what some are calling a "coup" against backbench rights and party traditions is that David Cameron did not do that.
Instead, Cameron organised and began a ballot not of the existing membership of the body he wished to persuade to change, but of the would-be membership of the new body he wished to create were his change to be accepted. In effect, the holding of his ballot abolished the existing 1922 Committee association, subject to ratification by the vote of his new all-MP group.
David Cameron won the vote by 168 votes to 118.
This means that 286 of the party's 305 MPs took part (with 19 MPs not casting a vote for or against).
Paul Goodman of ConservativeHome shows that this means David Cameron lost the backbench vote.
If all 76 Conservative Ministers had voted as instructed for the change, then that would make the backbench vote 92 for Cameron's proposal and 118 against the leader.
Even if we make a very pro-Cameron assumption, that there were no deliberate abstentions so that every single MP who did not take part was a frontbencher detained by ministerial duties, that would mean the 168 votes for the leader's proposal may have included only 59 Ministerial payroll votes rather than 76.
But the leader would still have lost the vote of his backbenchers: possibly by a narrower margin such as 109 to 118, though this would be wider if, for example, there were some deliberate abstentions on the proposal.
Unless Cameron has up to a dozen rebels in his Ministerial ranks, it is clear that he failed to win the confidence or support of his backbenchers in this ballot.
So Cameron won under his new rules, but he would have lost under the old ones. The Turkeys did not vote for Christmas - but fortunately for the leader his surprise new electoral college of Turkeys and Turkey Farmers did!
As Goodman writes:
Much of that goodwill has vanished since yesterday, driven out by resentment, grievance and anger. Tory MPs not usually prone to excitement are citing their leader in the same sentence as Kim Il Sung and Robert Mugabe".
That is excessive hyperbole, as the New Statesman says.
This was an altogether more British coup.
But you can't have a Clause Four moment by gerrymandering the rulebook because you can't win the argument.
Though clearly you can, when you have just lost the non-payroll backbench vote in your party, declare victory anyway.
If you are lucky, most people will believe you.