Nonsense. No Russian leader, least of all Putin, is going to commit suicide over an irrelevant naval base.
I take it you feel that Obama is somewhat less sane and is willing to commit suicide over a bunch of foreign nationals being killed in a civil war half a world away. If Russia and America start swinging at each other there is no guarantee who would be left standing.
There is no obligation on Russia to use force in defence of Syrians. There is indeed an obligation on Obama to use force if the Russians use force in defence of the Syrians. If the Russians launch an attack on the US fleet, the US will retaliate, 100%. The Russians know this. They also know how much force Obama can drop on their heads. Therefore, the Russians will not launch an attack.
Now, I think this is still stupid. Any strike on Syria will kill loads of Syrians. It will not save them, it will kill them. US credibility is not on the line: the US has, in the last decade, shown it will use force whenever it goddamn pleases, there is no need for a future demonstration. Furthermore, there is no international norm against chemical weapons use. The US government used banned chemical weapons in Fallujah without bombing Washington or arresting anyone (also, Saddam, too).