I remember in college we discussed a scenario much like
this but it was in the event of either of terror or a rare act of nature that would literally effect the entire North American Continent and it was an assignment we did
in combined psych/sociology class just after the Katrina fiasco. We settled on a EMP terrorist attack, where a nuclear device is detonated high in the atmosphere over the United States, which would render all unshielded electronics useless. You can probably imagine the chaos this would cause. We came up with some interesting conclusions, and I think you can apply some but not all of them to zombies as well.
I think it would be a bigger problem in the larger eastern cities, and especially bad East of the Mississippi, California, Texas(thanks to Mexico) and maybe the upper midwest/great lakes region. The southern states while heavily armed would have to deal with the influx of both refugees and zombies from all the urban cities on the eastern seaboard, and would be in chaos. Same with Texas and the border states which would be overrun with both refugees and zombies.
The midwest and plains states, rocky mountain states, and northwest would probably fare well, until the refugee problem starts coming their way. Canada with the exception of Ontario, Quebec, and and parts of British Columbia would do fare the same. Alaska while not having a problem with zombie populations would have problems when needed supplies from the lower 48 are cut off.
How would it get out of control? We can blame FEMA but the big problem will be the politicians of the urban areas who would refuse to bring the boot down and instead play politics with the problem. People in the large cities would finally realize that help isn't coming, or will come too late decide to flee to the countryside only to find the rural residents in full survival mode, and in no mood to welcome them.
FEMA/LE/US Gov - If the cities go bad most of the military and LE will be too busy protecting the rich, and connected. Other highly trained units will be hunkered down in various places with politicians, and military leaders and their families attempting to run whats left of the country from various fortified bunkers.The rest would be on high alert (most likely on ships, or locked down on bases) in case Russia or China decided to take the opportunity to get stupid with us (probably wouldn't qualify in a zombie scenario, but EMP it would be a real fear) and would be unable to help the civilian population in most cases.
It was an interesting assignment we were given and even had a handful of retired LE and military, social scientists, and economists give their opinions on what the US would be like if something shut the US down.
Btw pray a nuclear device is never ever detonated on US soil because it truly will be the end of the world as we know it forever. As one retired general put it, the US would have no choice but to retaliate against everyone and anyone with the capability of detonating a second or a third. It doesn't take much thought to realize how that scenario would pan out, and its chilling when you think about it.