What took the government so long to rebuild? Its the elephant in the room. Didn't they have continuity of government plans dating back a century to the cold war and nuclear attack? NEACAP, Looking-Glass, Boomers, Camp David, Raven Rock... Most reports even said the president himself survived so succession should have been a non-issue.
Well, truth be told, the problem was none of these things - but rather legitimacy and intimacy.
Its hard to say you're the government of the people if you take the hard stance and reconquer them with military force - if you have much military force left after the alien war and reanimate uprisings, and can get them deployed to the right places of course. Conversely, if you do too little, you seem to nothing but a pretender to the throne unable to actually affect anything. Perhaps worse - and to a great degree, what happened - is to seem unprepared next to local movements, and thus present little incentive to join the greater good.
The quick rise of city states was one of the biggest problems for national governments. Most people were used to Uncle Sam hovering over their shoulder in all sorts of little ways - from the currency, to the FCC regs on their computers, to traffic lights - even if you're just lulled into it being everyday life, you know someone's organized it. A lack of presence was felt quickly and hard, in turn allowing anyone who presented some stability seem wonderful in comparison. People quickly adopt an US vs Them mentality, and if the government didn't show itself quickly, others would take its place.
Furthermore, it must be remembered, that this wasn't a single great weapons exchange or natural disaster, but that reanimates and rouge aliens remained a threat for years to come, meaning the legitimate government had a war to fight in addition to rebuilding. In the old question of guns or butter, guns were undoubtedly needed.