You cannot be part of the EEA without subscribing to:
1. Free movement of labour
2. Most of EU environmental regulation and a lot of the economic ones.
What Cameron and company wants is to restrict these which means _LEAVING_ the EEA period. The Swiss which already heading down that route as a result of a botched referendum and will learn the consequences the hard way next year. One of the reasons why Eu will play hardball on that one is exactly that - Britain. We will all see exactly where happens as a result of restricting labour flow when this happens because Switherland currently has the same problems as UK and will get the same painful awakening which awaits UK in case of Brexit:
1. Their health system is run on more than 50% Eu labour. It will collapse overnight if this is withdrawn
2. Various services and non-banking parts of the economy similarly heavily use Eu labour.
It is all nice to have half of the banks in the world producing GDP (thought they usually hide it instead) when you are in an operating theater and the Romanian anaesthesiologist, German surgeon and Italian head nurse are not there to attend to you. While we can live without Bulgarian and Romanians washing our cars, that particular bit is a bit difficult to live without.
By the way - I am not being flippant here, when both of my kids were born, I did not notice any British natives at consultant level, there was on trainee doctor and some of the midwives. It was exactly the case of German surgeon, Romanian anaesthesiologist and Italian head nurse. So the observation that NHS is in the same boat (or worse) than the Swiss health service is a first hand one.