I've had TPT running on 2.8ghz Pentium 4s and on 1.86ghz Core 2 Duos, both with 2GB RAM (school PCs are terrible). Neither of these 'stuttered', despite being terrible CPUs.
What exactly do you mean by 'stutter'? What FPS are you getting on a blank screen? (also try tpt.setfpscap(1000) in the console and see what your max FPS is when the cap is removed)