Up until the collapse of the USSR most NATO countries had conscription, so basically all men served in the military for a couple of years in their late teens and early 20s.
Given the Red Army had huge forces in central Europe (they typically had around 400,000 troops in East Germany from the early 1950s until the late 1980s), NATO had to be prepared for a Soviet blitzkrieg at any moment.
West Germany's Bundeswehr, for example, used to have 500,000 personnel on active duty at any given time and 1000 tanks ready to be deployed. Now, the German army is down to around 180,000 and has maybe 50-100 tanks ready for immediate use. And their defense spending continues to decline.
Frankly, the Brits and French (the non-US backbone of NATO) aren't a whole lot better.
Libya 2011 - NATO couldn't handle a rather limited air campaign against Kaddafy's pitiful armed forces without needing the US to carry the day.
Even with Vlad Putin's aggressive foreign policy, NATO countries aren't in any mood to build their armed forces. Hell, there isn't a whole lot of enthusiasm for pretty tame economic sanctions.
Without the US, NATO doesn't exits.
The only consolation is that the Russian army is a pale imitation of it's Soviet Red Army forefathers.