No you don't need to spend money. I thought so too on my first attempt. Basically you can go back and race former opponents in the career mode to build up some cash. You can scroll left and right at both the "select a championship" screen and the "select an opponent" screen. The earliest opponents you can beat with a dead stock car.
I'm trapping 238 mph or so on the world championship level. Assuming I'm down to playing with settings to find that last 20 mph as I seem to have bought every advance mod possible. Definitely a fun game though.