Buddha had no master. He sat under a fig tree. Yet Zen practice - traditionally - would say you need a master, but it's open to interpretation. I practice Zen as well and sit zazen daily, and have been since about 2006. I would say no, it does not require a master, plus you have to think of the quality of master you would be able to find in the US.
There are many other sects of Buddhism that do not require a master. There are even a few sects that pretty much say "everyone is already Buddha and has Buddhahood inside them", and that you just need to practice to unlock it. Again, Buddha had no master, no scriptures, no texts, no nothing. He sat quietly and meditated, and eventually became enlightened one day under a fig tree, after vowing not to leave until it happened.
I read up on lots of Mahayana buddhism in general, and wouldn't call myself a strict Zen practioner. I find Buddhism in general very interesting, but I tend to stick with Mahayana because it seems more my style. I only follow for the practices and the writings/scriptures/koans, I do not take any of the mystical/spiritual/deity like portions to heart. But many sects would say you do not need a master. Take Nichiren Buddhism for example, which would say...
Many other sects of Buddhism, even within Mahayana, would consider this kind of a cop out. Nicheren's argument was that you don't need to treat a new buddhist pupil like a child, and spend all this time wasting on silly riddles and questions that have no answers, and that one can go straight to the Lotus Sutra where the actual knowledge is spelled out and more apparent, which makes sense to me. So I've read a few books from Nicheren teachers and that various associated texts with it.
Personally, I would say yes, Buddhahood can be attained by ones self, because Buddha himself did just that. To say that everyone else after him has to do it differently and under the watchful eye of a master is silly. Depending on what texts you read, most would say it took him six years to attain enlightenment, but it was extreme practice, and austerity of pretty much all things that lead him there. If he did it in six years without a master, I think the rest of us should be able to at least do it in our lifetimes.
I seek to emulate the practices and would love to be enlightened, but I don't see enlightenment ever happening in my hectic life. I simply don't think my modern lifestyle would allow enlightenment, but the practice can still bring me close, and bring a lot of value of mindfulness to my life. I've also taken removing vanity and ego as much as possible from my life, down to the point that I shave my head weekly as a part of my practice. That's what I seek, the practice and dedication to it. So I guess it's up to you, what you seek, and how you need to get there. For me, it's the journey, not the destination. The dedicated practice itself is the enlightenment.
Good luck, fellow Bodhisatta.