So, in case anyone is interested in an actual answer to this question, instead of OS holy wars:
The problem appears to be that the US-600 is not a class-compliant device - which means when you plug it into a computer, it doesn't present itself as one of the standardized USB device types. It shows up as a "vendor proprietary" class, so you have to install Tascam's drivers, such as they are. In 2015 there's really no excuse for that, but the US-600 is a few years old. Most newer, class-compliant interfaces will show up as an "audio" class device, and you won't need drivers because communication is handled by the OS (whether Windows, Mac, Linux, iOS, whatever).
Out of the units Tascam currently makes (which are class-compliant) the closest equivalent seems to be the US-366 - except it doesn't have MIDI. The US-4x4 is a lot more expensive... so we'll see what else comes along.
And, all OS bigotry aside, the question was asked about what DAW choices there are under Linux. There seem to be two major ones: a free, open source project called Ardour (which I haven't tried) and Bitwig Studio, which I bought and am running on both Windows and Ubuntu Linux. It looks/works a lot like Ableton Live, to the extent I've dived into it, and runs on Windows/Mac/Linux, so you have your choice. If nothing else, I found it to be a huge improvement over the lite version of Cubase that came with the US-600 - but yes, it costs money.