Cameron should say he's canceling his departure, call immediately for elections, says the Tories will run for a remain mandate and anyone in his party who wants the UK to exit to leave the party. He would win. UKIP would get some votes, but the conservatives would win because they'd get all the remain votes + those that regret voting leave + a bunch of labour votes since that party is in shambles.
Boris is out, Labour is out, all people would have left is to vote for UKIP, and they wouldn't win, and the UK could throw this whole Brexit thing in the trash since Cameron could say he won the mandate to stay.
The Tory party would cease to exist if he did that.
The idea of that happening would give me glee in any other circumstance but it would wreck the country. UKIP's ranks would be bolstered and a new right wing party would emerge from the Tory party's ashes and together they would form a coalition government.
If Cameron had the stomach for a fight he wouldn't have quit a week ago and he wouldn't have whined about immigration and pointed his finger at the EU a few days ago.