Not only did he apparently approve of and even commission hacking while a newspaper editor, he hired a private investigator who had been jailed for trying to plant drugs on other people (to create a newspaper scandal) and who later turned out to be an axe murderer. I don't mean that as a figure of speech; the fellow murdered his business partner with an axe. Now coulson did not know this was going to happen when he hired him, but Cameron (or at least his chief of staff) apparently knew about it before hiring Coulson and decided that he would make a fine addition to the team anyway, desite his extremely dodgy social circle. Add in the fact that Cameron has had a meeting with Murdoch or one of his top lieutenants on average every 2 weeks since becoming PM, at either 10 Downing Street or at Chequers (the PM's official country house, like Camp David for the President), and he looks uncomfortably close to a bunch of rather villainous people.
Remember that Cameron is governing as part of a coalition with the Liberal Democratic party, who are allied with him by necessity rather than by choice. If they pull out and Cameron loses a vote of confidence in Parliament, the government falls.