The Saudis will eventually fall, but thats not gone be anytime soon. If the carrot does not work anymore, they have the stick. Just look at Saddam, he was not popular but managed to remain in power for a long time. The Saudis have more money, and a easier to repress, less divided population.
The stick has to be paid too--otherwise things don't go very well for those who wield it. Saddam at least had enough of a domestic economy to tax to pay for the security services, as well as a loyal extended family that actually did some of the grunt work, whereas it is doubtful the Saudis have either.
The Saudis are sitting on the largest reserves in the world. They are profitable at the lowest prices. They have money for the stick and the carrot in excess and will be so long as oil has relevance.
> If the carrot does not work anymore, they have the stick.
Not really; while they've spent a lot of money of hardware to use as the stick, they House of Saud lacks the loyalty of enough of the population for the stick to be the primary control -- they need a lot of carrot to even keep the trigger fingers that would apply the stick on their side, which is a lot of the reason for all the accommodation the regime makes with religious extremists.
The Saudis will be fine for a long time.