Arm-chair generals here never fail to amaze me; they talk about nuclear war as if it is a matter of joke.
Even if USA and Russia engage in a conflict [Big If], it will be of limited scale and involve conventional weapons backed by lot of Psy-Op games to de-escalate the situation. For any country, nuclear war is a last resort option; this is true for even Russia. Even USSR was very trigger-conscious.
Also, Russia have a decent shelter structure because Russian military planners are fully aware that US nuclear delivery platforms are unrivalled in quality, efficiency and effectiveness and that large number of Russian assets are in massive danger of getting overwhelmed; in WCS, US is expected to launch an overwhelming conventional and nuclear barrage on all Russian assets to diminish much of the Russian offensive power early on. Number of missiles and atomic bombs is not the only factor; delivery systems and the tracking network are very important elements; US have the capability to track and target thousands of targets/locations simultaneously. <- This is not my personal assessment but gathered from consulting several sources about nuclear doctrines of big players and their respective strengths and weaknesses.
By the way, this thread is about Syria;
Assad is making a big mistake in current circumstances; he doesn't realizes that US may cripple Syrian military to great degree so that rebels would gain advantage. IMO, Assad should step down and set the stage for democratic reforms in his country; this is the only path to salvation for him. If Assad is expecting help from his allies against USA, he is fooling himself. At maximum, he may get some military equipment from Russia before this conflict takes place but this will not make much difference for him.