There has been some speculation about this recently and while just about anything is possible, there has been a fairly clear pattern in the revolutions of the Arab Spring.
The most vulnerable countries have been Westernized governments allied to the United States. The so-called dictators. The least vulnerable have been Islamic autocracies.
The rulers most likely to be overthrown were semi-secular governments in formerly stable countries who proved unwilling or unable to use their militaries to protect their rule. Those who were willing to shoot people in the street had less to worry about.
Gaddafi, who had shifted over to the American side of the board, was beating the insurgency until Obama, Cameron and Sarkozy came to the rescue of the Islamist rebels. Assad has still managed to hold out and may yet survive if the gang of three, with a new player in France, don’t come through.
Saudi Arabia has very little to worry about because its enormous oil wealth allows it to bribe sizable chunks of its own population and foreign leaders. That was something that Gaddafi was never good at, wasting money on various eccentric causes. The Saudis fund terror, but they fund American political leaders. They fund think tanks and university chairs, not soap factories for Farrakhan. Saif Gaddafi, the son of the madman, understood this and was beginning to cultivate those relationships and the safety that came with them, but he didn’t get far enough up the ladder.
While Gaddafi lost because of Western intervention, Saudi Arabia was given a free hand in putting down Iranian backed protests in Bahrain, with only a few words of criticism. There’s little doubt that Obama Inc. would give the Saudi monarchy even more leeway if it had to put down a domestic insurgency.
Then there’s the question of trajectory. No one on the Western side is likely to back a Shiite uprising and they don’t even have the numbers. The Muslim Brotherhood would love Saudi Arabia, but it doesn’t have the support to try something like that. Even its efforts in the UAE have gotten its tail nicked. Furthermore the Brotherhood’s Arab Spring was a Qatari project. And Qatar’s rulers aren’t about to push into Saudi Arabia. If the Brotherhood won, then Qatar would be next. If it lost, then the Saudis would find a way to make their Emir pay.
That just leaves Al Qaeda. A Salafist takeover of the Kingdom isn’t impossible, but it’s doubtful that the support is there. Twenty years from now when the oil revenues have dropped and the poverty level has grown and there are a lot more Islamist countries in the region, then Saudi Arabia might become a sitting duck, but even though it would have all that American firepower on its side.
Furthermore one of the reasons that the Saudis fund terrorism is to be able to control it enough to keep it away. That hasn’t always worked, but it’s worked pretty well considering the general lack of a serious domestic threat considering the sizable number of Saudi nationals involved in terrorism.
Saudi Arabia is still the petrofortress. It has bought more than enough influence to be protected and as long as its oil and money holds out, the House of Saud isn’t going anywhere.