Much of the president's speeches during his tour of the Middle East have involved rallying the Arab states to guard against the threat of Iran. However, according to Shibley Telhami at the Brookings Institution, Iran is indeed a threat to many Arab regimes, but not in the way you think. Although the article looks more at how Arab-Israeli peace making is the key to security rather than countering Iran, I'm going to focus on the disparity between the publics and their governments.
Its safe to say that there are more dictatorships disguised as democracies in the Middle East than there are actual democracies. Each of these regimes sees a common threat in Iran, Islamic fundamentalism. But they are not threatened by in the same way we here in the West are. The Iranian Revolution has been a scary thing for many nation states in the Middle East. Perhaps the only thing scarier than free elections for these governments is the idea of another Islamic revolution happening within their own borders.
The more the autocrats try to hold on to power by supressing the more radical Islamist movements, the stronger those movements become. And in many cases, as with Hamas and Hezbollah, those movements begin to provide the populations with what the government does not: hospitals, education, etc.
A US military presence is required to provide security for the governments, but as Telhami points out, those forces are not there with the mission to protect anything other than American interests. And then we come to a paradox. Military bases in the Middle East protect countries from militants (in theory at least) but the American presence creates a lot of resentment amongst the public and provides fuel for the militants who can say, "Look, Americans are everywhere, they're evil overlords who control everything." So the threat, or perceived threat amongst the people, isn't Iran, it us.
I don't have the answer to that puzzle yet. But I'll let you guys know when I do. In the meantime, add your own thoughts.