I'd assume the federal government would use every possible last resource available to save the capitol - drones - reserves - secret service etc.
Also, FEMA is located in D.C. and I'd imagine they also have huge medical and food reserves.
So best case, they got into bunkers and firebombed themselves? They made no effort (by the end) to save Atlanta, tried to just eradicate the problem, still fully zombie infested. I guess my question is: so what? what do you imagine the drones and secret service folks are going to do in this instance? Against about 10 million zombies within an hour's radius? And even if they got a little something going, are they still holding out 2 years later?
FEMA doesn't hoard their entire resources in a single building in DC, do they? Would imagine it's spread out all over the country, especially in areas where they predict they may need said resources. And if they've got enough onhand to support a couple natural disasters, how long does that last? In general, those resources are supposed to be deployable to last a week or so, maybe a little more, for a large number. They're only still holding out on them if you assume that almost everyone is dead, no?
In general, I just don't see it. You don't survive for years, much less thrive, in a former massive population center. To have any chance, government would have needed to fall back, and you attempt to retake the capital at a later date, once you've got a place to start from. Under siege, in the middle of the eastern seaboard isn't the place to start, and nothing useful or unique enough about DC to really suggest it's worth holding in that example.
And as people didn't know much about the ZA at the start, lots of places that could have been safe in a regular disaster were likely lost/compromised early. I know the comics are forcing us to go there, I just don't see how it makes any sense in a "real" ZA. Tell me that the safe zone is based around a decent military base in a sparsely populated Midwest state, I'm on board. Maybe Area 51 has enough infrastructure and a lack of people, although desert makes it kinda tough to otherwise survive. Or at least something defensible like Cheyenne Mountain, but half a million people in Colorado Springs. But I'd head for a base like that as a starting point to retake the country over DC every time. As long as they didn't screw up the initial ZA and get compromised, they've got a defendable base, military hardware and personnel, and not a ton of fresh zombies knocking on the door.
DC should just be a dead zone. Millions too many zombies wandering around to make it a viable place to survive. Not even if every secret service member is a Chuck Norris/Jack Bauer combo clone. Zombies just win on sheer numbers, lack of need for resources, and brute force.