a stock 3k can do statics in the dry (one wheelers, but hey) so if all you want to do is spin the treads, then just get the motor running properly. with the basic mods you're looking at (carb, cam, exhaust, head), i think you'll easily make at least 100hp, probably closer to 120, and that's plenty to make a decent smokeshow in an old corolla :)
christ, you could probably even blow off a camry! :P
just make sure you don't put good tires on the back, because the brakes suck so badly it's difficult to do a line lockie with power. mine just locks the fronts and pushes the car along. of course, you could just weld the diff, problem solved ;)