The government isn't ignoring public opinion. Would that life was a simple as some people wish. In the UK there is a separation between the executive and the judiciary. Once a law is passed, the people who implement it are the judiciary and the executive has no say in its execution (with the exception of the Home-Secretary's powers to vary sentences once a conviction has been made).
That's why the Home Secretary said today that he had no power to stop the extradition, and that if he attempted to block it he would be acting illegally.
Yes, the law is probably faulty - and the CPS should have acted sooner to try McKinnon in the UK - as other hackers have been - but it can't be changed without the consent of Parliament.
Cameron, for all his grandstanding, knows this full well, which is why his stance is particularly hypocritical.
I don't think any politician of any stripe wants to see McKinnon hung out to dry, but the matter is out of their hands.
The Daily Mail - no friend of the Government - has written:
In her letter to Mrs Sharp [McKinnon's mother], Mrs Brown said 'that there are a number of people at Downing Street who are committed to following the case and providing what assistance they can'.
However Government sources said last night that while the Prime Minister 'understood the family's concerns', it would be 'difficult to intervene in the legal process'.

And, although the law apparently unfair in that the US does not have to present a prima facie case to justify extradition, McKinnon's particular predicament is an inappropriate one with which to argue the point. He has openly admitted what he did so there is no question of ambiguity or weak evidence - the man himself has said he what he did and, when arrested and questioned, said he would do it again. One of the messages he left on a US system, he admits, read: 'U.S. foreign policy is akin to government-sponsored terrorism these days ... It was not a mistake that there was a huge security stand-down on September 11 last year... I am SOLO. I will continue to disrupt at the highest levels.'
Asperger's notwithstanding, the man has done himself no favours at all. Naivete, foolishness, vainglory or even arrant stupidity are no defence in law.