Lawyers have dubbed the first working day of the New Year “divorce day”, as couples rush for advice on separations in the wake of Christmas rows. By startling contrast, the Prime Minister and Deputy Prime Minister chose this week to reaffirm their commitment to each other, though both were keen to stress that theirs is a “deal” rather than a “marriage”.

Both party leaders were at pains to present the Coalition as “steadfast and united”, but the relaxed and convivial atmosphere of the joint press conference was slightly soured by the actions of senior political figures who seemed anything but. Former schools minister Sarah Teather announced her intention to vote against the government’s 1% cap on benefits, and Tory grandee Lord Strathclyde resigned as leader of the House of Lords in frustration at the unwillingness of Lib Dem Peers to tow the party line.

Commentators and Labour will be looking to widen the cracks of disunity. And figures like Tim Farron on the Lib Dem benches and Peter Bone from the Conservative side are loudly supporting differentiation strategies in which both parties can see other people for a while – UKIP, perhaps, in Peter Bone’s case. So does anyone buy this unity at the heart of the Coalition pitch? Is it credible?

Despite dissenting voices, unity where real power gets shared is more important to the government programme than unity under any one political banner. Cameron and Clegg face similar challenges in keeping their parties behind them in the run up to the 2015 election. But their mutually dependent personal futures are more than enough to bind these similar characters from similar backgrounds, who reportedly get on well. Their unity of leadership will be enough to see Coalition Mark II take on some meaty political challenges – the reform of welfare and payment for long-term care for example – regardless of resignations and rebellions.

Disunity within political parties is part and parcel of the party system. The Lib Dems tacitly recognise this in their election strategy, with their 57 MPs expected to fight 57 different election battles in 2015 (see the weekend’s Guardian on this). And the Tory Right would oppose Cameron’s ideals even had he won the 2010 election outright. It may not stand either of them in good stead for a second term, but “steadfast and united” leadership should outweigh wavering and inconsistent memberships – at least for now.