I'm a long time user of TabIt, and have used Crossover and Linux for even longer. Currently I'm running Debian Squeeze AMD64, and I just wanted to document the ease of which I got Tabit running under Crossover Games and Professional.
To start, you need a couple prerequisites on your Debian system. You can get these through apt. This is actually the hard part. Once I figured out what the midi requirements/dependencies were, the TabIt install was less than trivial.
:~# apt-get install timidity timidity-daemon pmidi fluid-soundfont-gm fluid-soundfont-gs freepats
Now just install Tabit as an unsupported application, and you should be ready to do some tabbing in Linux.
FYI, I run all my Crossover apps in a Window because I use XFCE4, and if I don't, it causes flickering. So if you're having any display issue, try running it in a window.
To do this, select "Manage Bottles" from your CX menu. Select the bottle of the app in question, then select the "Control Panel" tab. Under "Control Panel" select "Wine Configuration" and it will give you a Windows interface. In that interface, select the "Graphics" tab, and click the "Emulate a virtual desktop" box. Select OK and you should be ready to use the TabIt app. I know this is redundant being on Codeweavers site, but hopefully it will speed up the process for anyone wanting to run this app.