Will the UK coalition government unravel?

I was watching a BBC interview with Lib Dem MP Simon Hughes yesterday and I was wondering if the UK coalition government will unravel. He made a good job batting away a question about a possible graduate tax but then was asked about the Iraq war.
Perhaps his reply was not helpful to the coalition government but shows up the differences in the administration. Hughes said all Lib Dem MPs thought the war was illegal.

The UK coalition government has to get on with the situation as it is now. The aim must be to extricate our troops from fighting abroad rather than worrying about the illegality of the Iraq war, which is just too late.

It is amazing that the Labour Party is taking so long in selecting a leader, when the coalition government could do with some external rather than internal opposition.
For instance, Andy Burnham should be leading the attack on the government plans for the NHS, which represent quite a gamble.