For Saudi Arabia the deal with America is that the House of Saud get to stay in power in exchange for the oil, it is that simple. If there is this 'uprising' that you speak of then it will be Uncle Sam's job to put it down.
The original deal goes back to the time when Britain was supposed to have Iran and the U.S was supposed to have Saudi Arabia. On the back of this deal the Saudi 'Royal Family' have built some myth of entitlement to the throne and being a proper 'royal family'. It is an illusion, there is no legitimacy there. So long as they wear the 'traditional' outfits and keep the 'traditional' laws nobody is going to see that the emperor has no clothes.
I don't get the impression that there is any type of organisation against this so-called 'royal family' with a class of people clued up as to how to live in a non-feudal society. They are far from socialist, mere serfs in an offshoot of empire, relatively rich because that is where the oil comes from. They never had industrial capitalism, they went straight from sand and a bit of tourism revenue to the monster of finance capitalism, trickledown economics and everything that the IMF demands. Because of the oil they do get a few empty gifts from the system such as cheap petrol.
For decades those dollars have flowed back to the West in arms sales. To an extent this clawing back of the money has also happened with luxury goods too. So the serf-grade workers of Saudi Arabia are doubly screwed, when this imaginary 'uprising' happens and they impose a government that 'shares the wealth' they will find it has all been spent on underground aircraft hangars and bits of paper that are allegedly investments in the Western stock market.
My favourite fact regarding oil is how it all went wrong in the 1970's with the oil crisis. What only a careful reading of the Wikipedia article tells you is that the US increased grain prices 300% to pay for Vietnam. This was bad news for the OPEC countries, places like Iran had kind of got used to affordable wheat. This wheat had kind of covered the U.S. balance of payments for oil imports before Vietnam, so it had been a happy arrangement. Our history tells the 1970's oil crisis very differently, forgetting the wheat price hikes.
As the article states the government can make quite a few concessions, e.g. women driving, allowing people to go to the theatre, that sort of thing. They can buy off those that might resent how things are going by these concessions yet still keep a tight grip on the deal which is essentially oil for arms and food.