Yes, it falls a bit flat.
David Cameron fibs to cover his butt, like every politician in history.
The joke works better when applied to someone who had a whole team of spin doctors to continually distort the truth, repeatedly misled Parliament, cost the lives of hundreds of soldiers and civilians through his willingness to lie to the nation, etc.
Hence, it was a bit funnier with "Tony Blair".
With "David Cameron" it just sounds a bit like a Party Political Broadcast On Behalf Of The Labour Party.