Well, my current pessimistic expectations are that, within the next year or two, we're going to have direct clashes between Syrian government forces & Russian air support vs FSA & USA spec ops with Coalition air support, which will quite probably result in a declaration and an attempt to enforce a no-fly zone over the entirety of Syria, which is almost immediately followed by a direct confrontation between Russian and Coalition air forces, potentially starting off a conventional phase of a WW3.
Syria isn't important enough, a war between Russia and the US could only start under those circumstances if both sides wanted it (or one side really wanted it). Even if the US military shot down a Russian plane in broad daylight, one of the governments would need to be willing to declare war for anything to come of it, and I think that's extremely unlikely.
Sticking to the anti-Assad stance is more a matter of embarrassment for the US, and in that respect Russia is on track to inflict a minor humiliation out of this. Assad just happened to be on the US government's shitlist for harboring anti-Israel terrorists, him gassing civilians and committing other atrocities would be forgotten very quickly if he does end up pulling through this.
The thing is, if Putin decides to concede an American attack on Russian military forces, it'll be political suicide for him. This isn't comparable with Turkey shooting down one Russian fighter at the border - that was a minor border incident. No one among anti-Western political forces and their supporters will ever forgive conceding a deliberate attack by the United States - he'll lose a very big chunk of his popular support. So I think a war between Russians and Americans in Syria can only result in one thing - further escalation.
And to make things worse, the most likely next American president has always been itching for a fight against Russia in Syria. Looks like the next 4 years will be incredibly
!!fun!!