Nick Clegg has dismissed jibes from Tory Education Secretary Michael Gove that he cannot make up his mind whether he supports school reforms.
The Deputy Prime Minister insisted parents "couldn't give a damn" about internal Government spats as long as the education system is improving.
But he repeatedly refused to agree that Mr Gove was doing a good job, instead crediting the wider coalition for introducing key policies.
Relations between the Liberal Democrat leader and the Conservative Cabinet minister have been strained for some time, with Mr Clegg criticising the use of unqualified teachers and blocking plans to increase child-to-staff ratios in nurseries.
Tensions were heightened last week when Lib Dem schools minister David Laws criticised Mr Gove over the decision not to retain Labour peer Baroness Morgan as head of Ofsted.
In a Telegraph podcast, Mr Gove said Mr Clegg had an angel sitting on one shoulder that backed the controversial shake-up while a "bad" force was urging him to indulge radical Lib Dems.
"There will be some people in the Lib Dems who will want to emphasise those differences to appeal to a section of the electorate that voted for the Lib Dems in the past, but don't agree with the changes we are making to the education system now," Mr Gove said.
" Good Nick, the angel on one shoulder, is saying 'What Gove is doing is socially progressive, socially mobile, and in tune with good old Gladstonian principles'.
"Wicked Nick, sitting on his other shoulder, is saying 'Yes! But some of your more radical activists dislike it, so pander to them'," he said. "He will have to decide whether it's the good or the bad Nick that he indulges."
Speaking on his regular LBC radio phone-in, Mr Clegg joked that both his shoulders "speak in perfect harmony".
"I think parents listening to this just couldn't give a damn about what one politician says to another when it comes to the schooling of their kids. What they want is good schools," he said.
"I just think parents want politicians to get the basics right in education."
Pressed on whether he thought Mr Gove had done a good job, the Deputy Prime Minister replied: "I think we as a Government have done some really, really good things."
Mr Clegg said he was "not worked up" about whether particular individuals stayed in roles such as heading Ofsted, but insisted appointments had to be based on merit rather than political allegiance .