Is it support or is it fear of a ruthless dictatorship that has a huge internal security apparatus to crush opposition? Just as with Gaddafi or any dictator, it's pretty meaningless to talk about support of the population. If you don't support the dictator, you're imprisoned, tortured and/or killed.and it has to be reiterated the Syrian Arab Army is majority Sunni. Without the support of his Sunni fellow citizens Assad would have been gone long ago.
I'd say the main reason Assad has survived so far isn't because of "support" of his Sunni fellow citizens, but "support" from Hez & Iranian fighters & Putin.