The D600 has been supported since LR 5.0. What version of LR do you have? You may need to add or remote a memory card in the camera, depending on whether you don’t or do have one in, now.
I have lightroom 5.7 .
I am having the same problem with both my D610 and my D800. Both worked fine in the past. In both cases, I can import files from the camera via 'Import', so I know the USB connection to the computer is fine, but Neither camera is detected during tether.
Mac OSX 10.10.2 and LR 5.7