Of course, it all depends on your definition of 'great turntable'. I'd say a good enough turntable is definitely possible to build for under $2,000.
For example, you could hunt for a used Systemdek IIX. Off the shelf maybe not that fantastic, but it is endlessly tweakable, and you can quite easily nudge it to the very respectable level for very little investment.
I have tried it with Jelco 750E 10" tonearm, and it sounds stunning. Jelco will give you the ability to try out various mid-to-high-range cartridges, so you won't be limited in that area (I'm currently using Denon DL-103 and Ortofon OM20). I'm mating Jelco with Nagaoka cables, which is an awesome upgrade.
Lastly, you can top it off with iFi Micro iPhono 2 preamp and still won't break the bank. iFi iPhono 2 is maybe the best bang for the buck I've seen lately (but don't bother with iPhono 1, it's not nearly as good at 2). It will give you that much coveted 'silky' and deeply sonorous sound that I was previously only able to hear with seriously expensive phono stage.
With the above configuration, I am convinced that you will be able to give more expensive turntables a good run for their money. Of course, you won't be able to beat ultra high end gear, but for the meagre $2,000 or so you're sitting in a very respectable audiophile position. Nothing to scoff at.
