I was discussing with a friend recently why the Saudis are so worried about Mubarak's fall that they would offer to pay Egypt's aid if the US cuts it off. I doubt they are worried about Saudis taking to the streets - Saudi Arabia is not only a kingdom, as opposed to a dictatorship pretending to be a democratic republic - the country is actually named after the ruling family, the House of Saud.
Rather, I think it is all about Iran. I would guess that Saudi Arabia has the second greatest interest after Israel in making the Israel-Egypt peace agreement and military cooperation hold, ahead even of the US. On January 24 they had an alliance with Egypt, who had an alliance w/ Israel, creating an unofficial Saudi-Egypt-Israel alliance to balance the Iran-Syria-Hezbollah axis. I am reasonably confident that the Saudis have been coordinating with Israel at some level - via Egypt - on how to contain Iran and what would happen if there was a war. Imagine what the world looks like to the Saudi royal family after the US has removed combat forces from Iraq and the Egypt link in the Saudi-Egypt-Israel alliance breaks? Their military is not very well regarded, and they're potentially facing a Shi'a arc w/o the backing of the two militaries that could provide deterrence (they would still maintain a backchannel connection with Israel on defense issues, but it would be much more difficult).
For this reason I also bet the Saudi royal family wants Israel to have a peace agreement with Palestinians more than anyone else in the whole middle east (including Israel and the Palestinians) - so that they can openly form an alliance with Israel against Iran w/o looking like traitors to the "Arab street." In fact, if Egypt broke its military alliance with Israel, I would not be surprised to see the Saudis step up their peacemaking efforts dramatically, or see them ignore public opinion to sign an agreement with Israel even without an Israeli-Palestinian agreement (they would just have to launch a propaganda campaign justifying it as necessary to defend against Iran and/or shift their public bogeyman from Israel to Iran - think about how the US created propaganda showing the Soviets as allies during WWII).