But look at this. According to this piece in Reuters, Egyptian Muslim Brotherhood has now officially come out supporting the Jihad in Syria. Given the Brotherhood's history, this isn't terribly surprising. But remember, the Brotherhood is the ruling party in Egypt. Meanwhile, this article says that President Morsi's office is saying quite explicitly that his government will take no action against Egyptians who go to Syria to join the fight. Meanwhile Morsi himself is scheduled "to attend a large rally in support of the Syrian opposition at Cairo's stadium on Saturday, which has been organized by the senior clerics."
I'd defer (and like to hear from) region experts. But this is starting to sound like Syria's going to become some version of what Afghanistan was in 1980s - a magnet for young Sunni Arab men who want to fight in the Jihad. Only Syria is really close to the Arab heartland states. Obviously it's one of them. And the key Shia army in the fight is actually based in Lebanon.