According to a report in the Guardian, the complex political make-up of Syria and the lack of truly effective opposition ground forces in the country make air strikes more difficult.
The parliamentary vote against taking on Assad's regime last summer also means Cameron would need to propose a new motion in the House of Commons.
What are the drawbacks?
The welfare of British citizens Alan Henning and John Cantlie will be of concern to the government. Isis's previous hostage murders, including that of Frenchman Herve Goudel yesterday by a linked jihadist group, were all said to be acts of retaliation to Western military operations.
Ghaffar Hussein, the managing director of the Quilliam Foundation, has also warned that using such force against Isis in Iraq and Syria means a terrorist attack in Europe or the US becomes "almost inevitable".
"This [these air strikes] is a game changer for Isis. They are being backed into a corner and there’s nothing they can do about it," he told i100 .
"They don't have sufficient anti-aircraft weaponry and won't be able to react in a conventional way. All they have left now, apart from upping the anti in terms of propaganda, is to target terrorist attacks around the world."
This is not to mention the moral and legal questions arising out of such a campaign. And as Andreas Whittam Smith highlights in today's Independent: "badly designed military action could make matters worse rather than better".
Will air strikes be effective?
Despite six weeks of bombing in Iraq, the US has still failed to significantly weaken Isis's grip, according to the New York Times .
The Independent's Middle East correspondent Patrick Cockburn also raises his doubts today, and explains that air campaigns "do not win wars on their own". A point backed up by the Independent's defence correspondent Kim Sengupta.
Will ground troops be sent in?
No, there will be "no boots on the ground", according to Cameron. Interestingly, despite the loss of over 600 British soldiers in Iraq and Afghanistan in the last decade, this poll by YouGov (below) suggests that 29 per cent of the public would support a ground operation, with a further 18 per cent not ruling out the possibility.
What have the leaders said?
Isolation and withdrawing from a problem like Isil will only make things worse. We must not allow past mistakes to become an excuse for indifference or inaction. The right lesson is that we should act – but act differently [to the 2003 Iraq War].
It [Isis] is a murderous organisation, has taken British hostages, threatens the stability of the region and is therefore a threat to the UK’s national interest.