No it's possible. What you need is a Diamond Multimedia BVU195 (which I use to provide dual displays for my MBP - both displays are 24" 1920x1200). But it does cost $75 or so. There is a BVU160 that displays a lower resolution like 1280x1024 that's a little cheaper.
USB video is totally usable. I connect one monitor to the BVU195 and use it for web/mail/document editting. I acutually have it pivotted so I display 1200x1920, no problem.
I don't know what gpu is on a EEEpc, I assume just GMA900 or X3100 or something like that. The 8600M in my MBP is quite a bit more powerful but I don't know if USB displays use the onboard GPU.