Putin has reportedly informed Turkey (and presumably the Saudis and US) that a Turkish/Saudi invasion that threatens Russian forces in Syria is illegal (this is true) and will be met with tactical nuclear weapons (this is alarming, but may in fact be technically legal under such circumstances).
So Erdogan's only card is calling on NATO to back him up. That's World War III right there, unless somehow the world pretends a tactical nuclear weapon didn't just vaporize some large number of Turkish troops and armaments.
Being a member of NATO is not supposed to be a license to invade sovereign countries, though, (which is what Syria remains, like it or not) just because the U.S. has your back. My guess is that Obama won't want to see his children vaporized by a 90-megaton submarine-launched Russian warhead, though, and things will cool down after much saber-rattling.
Still not a good idea to ratchet tensions to that level. Erdogan is a corrupt asshole.