I don't understand why people are saying milenia... I'm sure things were much worse in the days after the fall of rome (sure, there's no fallout, but there's not the same level of tech either).
Theres also no deathclaws, Supermutants, lack of food, radiation hotspots, roaming military robots armed with miniguns and missile launchers, ect. I'd say the Fallout Universe has it alot worse than the days after the fall of Rome....
You are confusing a nuclear accident with a nuclear armageddon. A total nuclear war would result in the extinction of most life on the planet. It's why it's so feared. There would be some life but not much. The radiation might not last for years but nuclear winter would. All the ash and dust from the fires caused by the nukes would stay in the atmosphere for decadeds.
Fallout Two intro: War, war never changes. The end of the world occurred pretty much as we predicted, to many humans not enough space or resources to go around. The details are pointless and trivial, the reasons as always purely human ones. The earth was nearly wiped clean of life, a great cleansing. An atomic spark struck by human hands quickly ragged out of control. Spears of nuclear fire rained from the skies, continents swallowed in flames and fell beneath the boiling oceans. Humanity was almost extinguished, their spirits becoming part of the background radiation that blanketed the earth. A quite darkness fell across the planet, lasting many years.
Nuclear Winter is a debated theory. In the book Nuclear War Survival Skills written (a Civil Defense book written by Cresson Kearny), it states that temperatures would only decrease around 20 degrees for just a few days as opposed to years....
Of course there is no real way of knowing without nuking the planet.
On topic: I doubt it would take centuries or millenia for America to go back to "normal" in the sense of a unified country with law, police force, and government. Why? The NCR seems to be strong enough to take control of the West Coast and more, especially if an alliance could be formed with the BoS. On the East Coast, the BoS learns of the source of the Supermutants (if you tell them of course) and would more than likely eliminate it, thus eliminating the only major threat to the BoS. After years of expansion, the Lyons BoS should have unified DC, and if they aquired the Pitt, then the rest of the East due to their ability to produce ammunition now (and possibly weapons/other equipment).