An article in tomorrow's Observer suggests that this may happen.
Toby Helm and Daniel Boffey write:
Nick Clegg, the deputy prime minister, has refused to give unequivocal backing to Jeremy Hunt over his handling of the BSkyB takeover controversy as senior Liberal Democrats broke ranks to demand a new investigation into whether the culture secretary has broken the ministerial code. ...
Labour will call a Commons vote on whether Hunt should be investigated, claiming he misled parliament about his role in News Corp's bid for BSkyB and failed to keep his adviser Adam Smith, who quit over his contacts with Murdoch executives, under control.
A Lib Dem spokesman refused to say whether Clegg would order his MPs to back Cameron. "No decision has been taken," he said.They go on to name three Liberal Democrat parliamentarians who have publicly criticised Hunt: Adrian Sanders, Lorely Burt and Matthew Oakeshott.