I don't know if anyone has read World War Z
by Max Brooks, but that book posits a number or reasons why a modern military would fail to hold ground (at least initially) against a world overrun by shambling corpses. I think there's a couple of chapters on the experiences of a US soldier who fought all the way through. There's all sorts about how bombs, heavy machine guns and flechette launchers were worse than useless as for the most part, all they'd do is shred the body and blow off limbs with only a small proportion getting adequate head-shots.
Hell even nukes would be of limited, if any use since they'd "only" incinerate the walkers within a few miles radius. Beyond that it's "just" various degrees of burns and radiation exposure. Even if you hit a densely infested area like say a major city, unless you're willing to carpet nuke the whole place and spread fallout over half the continent, all a single nuke will do it take out maybe ten thousand. The population of NYC is what? 8 million? Even with an optimistically low infection ratio that's a hell of a lot of zombies.
Now imagine cities like Tokyo, New Delhi and Seoul; really high density population with that kind of rampant infection and then imagine what happens when they run out of the living and start spreading out through the surrounding countryside. It's no wonder the military wouldn't be able to hold against those numbers. After all, what good is a tank if the enemy can't be intimidated and will just swarm over minefields, defensive lines and razor wire, no matter how many of their fellows they have to climb over. As we saw in the opening episodes, you may be safe inside a tank, but you can't exactly stay in the thing forever.
From what I've seen of the show so far I suspect the show writers (and possibly the original comic writers) have read that book as it all seams about in line with the book's period after "the great panic." Basically by this point I imagine the bulk of the surviving military has fallen back to remote defensible positions in the north where they can dig in and wait for winter. Everyone else would be basically left to fend for themselves and the fall back positions would be kept secret to prevent stragglers and refugees bringing the horde to their doorstep.