It depends on what you mean by cheap fixed gear. Stay away from the "fashion brand" types that market super sweet fixie colors, bro!! Purefix is a great example. Horrible frames and components.

I got back into cycling on a cheap Bikesdirect fixed gear. I think it was $250 at the time, but this was also right as fixed gear bikes were really turning into a marketable niche, prices have probably gone up since. The frame and components were still entry level-ish (tires and saddle being complete rubbish), but a nice step up from the trash on the market nowadays, which can be hard to avoid.