IMHO people have lost sight of what this mission will be, particularly the British public. Obama has no desire whatsoever to get embroiled in a long-standing involvement in Syria. His actions would be a 2/3 days strike involving 20/30 missiles maximum, hitting Assad's capabilities in a sort of 'now play nice' initiative, nothing more than that.
In all probability it will limit his (Assad) potential and allow forces opposed to him to at least get a foothold in key areas. As he (Obama) said, it is not his task to bring about a regime change, that is for the Syrians to thrash out, however unpalatable it may be. It will not happen overnight and may take 10 years, or even longer.
It will though allow those opposed to Assad to potentially force him into some sort of dialogue or talks, which is what the West ultimately wants.
The UK are fed up of seeing their troops brought home in coffins (and rightly so) or their Servicemen increasingly in the news with missing limbs etc.
They have reservations about mission creep, which invariably is a possibility but I believe that UK troops would never have set foot on Syrian soil anyway (we do not presently have the capability), which had Cameron made a public caveat would have possibly ensured his motion carried in last week's vote.
His failure to make such limitations ensured the loss in the Commons.
It is now somewhat decidedly ironic that the US's biggest ally in all of this will be the 'cheese eating surrender monkeys' and the UK has indeed been seriously diminished, as Lord Ashdown says.
Just my take on things, don't flame me please!!