Well for starters the most rural and suburban areas should be able to handle themselves fairly easy. Sure during the initial outbreak things will be messy, but combined with the proliferation of arms and a spread out population, it would be much easier to round up people into groups and start clearing the area of zombies. This as well as the fact that most towns of a reasonable size will have national guard and reservists as well as police to help organize settle things.
Even in liberal LA you still have alot of gun owners. At least 50% of american households have firearms. Obviously that rate is significantly higher depending upon where you live. In dense urban (verticle sprawl) type cities like NY gun ownership might be as low as 25% of households (due to strict gun control laws and lots of libs), but even LA you can bet its 50% and in places like texas its probably around 80%.
Now considering this, you can bet that all but the mega metropolitan areas will be able to deal with the outbreak. So lets say a few weeks after the outbreak those major cities like NYC are completely dead and millions of zombies are pouring east. Well that zombie horde is going to be heading into very flat and open terrain which makes them an easy target for the armed forces to contain. After all if citizen militias in rural and suburbia can easily handle an outbreak in their area, then that frees up the army/airforce to focus on containing the giant hordes in the mega cities.
10 million zombies might seem like alot, but huge slow moving masses on open terrain would be an airforce pilot's wet dream. If there is one thing the US military can do, its deliver a ton of munitions to a target. You would have B-52s carpet bombing the out of these hordes from low altitude as well as army firebases pounding them with artillery. Any remanent zombies that manage to make it through that kind of bombardment would be easy prey for soldiers and civilian militias on the ground.
So its extremely unlikely that I would be facing 100,000 zombies by myself.
A) I can arm alot of people to help me defend
B) There are around 1.5 million people in my state. 500,000 of which live in the surrounding valley I live in. Of which you can easily bet 65-80% of the households have at least one firearm. Hell I could perch myself on my roof and pick off hundreds of zombies in an afternoon. If even 5% of us managed to do the same then we would be fine.
The biggest problem in a zombie apocalypse for largely unarmed nations is not the zombies, but starvation. Finding some high ground where clumsy zombies can't access is relatively easy, but when the zombies mass you will find yourself besieged and with no firearms, breaking out of such a situation would be far too risky. So you sit there and watch as your food supplies dwindle.
So the US would likely be safe within a matter of a few months. The real problem lies at our southern boarder. The trick would be to clear the US and shore up our southern boarder fast enough before the giant hordes of zombie Latinos stream north. Those nations south of the US are largely unarmed outside of the military( which are small and underfunded at best), so they would probably all die fairly rapidly.