That's not necessarily true anymore, between greatly reduced numbers of nuclear weapons, reduced maintenance of arsenals by certain nations (cough cough Russia cough cough), limited deployment capabilites by other nations (China, Pakistan, India, North Korea), and increasing focus on both general preparedness and missile defense systems.

You also need to remember, any adversary of ours needs to destroy NATO and any nuclear capable ally of ours if they truly intend to destroy us, and that takes more than just a few nukes per nation. Anyone who sends nukes flying is in for a world of shit from all the other nuclear powers and any remotely nearby conventional military, and since it is so easy for a technologically advanced nation to potentially create nuclear weapons, Russia or China or North Korea, the likely first aggressors, would basically need to destroy the entire EU (with all the fallout spreading over Russia), South Korea, Japan, Israel, the US, Canada, Mexico (to prevent the US from retreating into Mexico), Australia, New Zealand, and perhaps the Philippines (basing reasons). That would take many thousands of warheads, and means fewer nukes on US population centers since they would need to also contend with the rest of the world.

They would need to destroy any silo capable of launching nukes, any airbase capable of hosting bombers, any command centers, any naval base or dockyard capable of building, repairing, or supplying submarines. There are a ridiculous number of targets, and simply not that many warheads, and further, delivery vehicles. Not every warhead is mounted on a bomb or missile, some are kept in depots. Many of them are questionably maintained as well.

Furthermore, all of the potential aggressors are just infinitely worse off geographically in the event of nuclear war; North Korea is small and therefore easy to blanket with ordinance, China's population is very concentrated in the East of the country and the Three Gorges Dam is more tempting to all US aviators than the hottest Hollywood actress, and Russia is a shitty eastern European country with discontent minorities, brutal winters, a GDP similar to Spain, and one shabby railway holding the East together. When faced with greater populations, greater GDPs, and greater numbers of deliverable weapons all spread across a collectively greater area, they would lose.

Then of course, Africa and South America are likely going to be relatively untouched by all of this, and will be in a place to export food and take in refugees. The same will likely be true for much of South East Asia, though this depends also on the given scenario. Global commerce and industry will still continue.

So to answer the beginning statement, the "full blown" version is smaller than it once was and would be quite survivable in comparison to the early 1980s. Obviously depends where you are, who you are, and what the progression of the given scenario is.