To say there is a rift is probably putting it too strongly. But is Downing Street on the same page as the military when they talk about Syria? No, it isn't.
The fact that General Sir David Richards, chief of defence staff, has been drawing up contingency plans to provide Syrian rebels with maritime and possible air support should not be seen as an appetite within the Ministry of Defence to get involved.
The military might well do; it might have to. But it doesn't want to, at all, and for months military sources in Whitehall have been expressing deep unease about the situation to anyone who will listen.
Their concern is that David Cameron isn't one of them. Buoyed by the success of the very limited campaign in Libya, and horrified by the plight of refugees he met on the Syrian-Jordan border last month, the prime minister has got a slight case of what some in Whitehall call "foreign fever". Cameron wants "to do something", they say, though he is not exactly sure what that something should be.
Last month, fresh from his visit to the Middle East, the prime minister chaired a National Security Council meeting in which Richards set out some of the problems and possibilities posed by the Syrian civil war.
Richards made it clear that a full-scale intervention, of the kind that took place in Iraq or Afghanistan, was deeply unappealing and would require a massive build-up of naval forces in the region to neutralise President Bashar al-Assad's anti-aircraft missile batteries.
There are differences of opinion among experts about just how strong they are, but the MoD's analysis is that they are fearsome – with officials pointing to the Turkish fighter downed earlier this year on the periphery of Syria's airspace.
The received military wisdom is that a prerequisite of any large-scale military involvement would have to be the establishment of a no-fly zone. This would require a long aerial campaign launched from aircraft carriers – and Britain will not have one available until 2018.
Other options are all speculative, such as safe corridors to refugee camps in Turkey, or in the north of Syria, and logistical help for the rebels.
Interestingly, Richards's presentation apparently did not include any reference to Nato, or to how it could co-ordinate a military response.
Though nobody will talk about this in public, it seems the meeting did not completely douse Cameron's desire for the UK to take a lead, which is why Richards has been beavering away on a range of other contingency plans.
This is understood to have included chairing a meeting with senior military figures from France, the US, Turkey, Jordan and the Gulf states of Qatar and the United Arab Emirates, which, with Saudi Arabia, has been in the vanguard of those supporting the Syrian rebels.
In his public utterances Richards has remained open minded, as he must, saying it is "not impossible" that UK forces could be involved in some very limited way.
Ultimately, any decision to act over Syria will be a political one, not his, and he does not want to back himself into a corner.
But nothing has changed the military's reluctance to get involved in the Syrian crisis. Officers insist there must be clear and united political will over what to do before troops are committed – and they want a robust and well thought-out exit strategy. Neither exists at the moment. The only scenario that would prompt the military into immediate action is the use of chemical weapons by Assad, or the prospect that some of them might end up in the wrong hands if his regime can longer protect them. At that point the UK would undoubtedly contribute to special forces operations to secure those weapons, following a US lead.
Until then Richards will have to continue his slightly awkward tap dance in front of the prime minister. Offering some ideas, without committing to any of them, and cautioning that involving even a small number of British troops to a fourth campaign in a decade, at a time of restructuring and redundancy of the armed forces, in a region where the UK is not regarded as an honest broker, might be more trouble than it is worth.