That's Travis the helpful everybody.
Let's hear it for Travis.
It is possible (heck for some, even easy) to code the behavior in a 2D Game. What you have to address is traction of the vehicle, and then work out a point where you break traction. That is easy enough. The hard part is working on balance of the car.
You will most likely want to track a variable for wheel spin and using traction, speed and acceleration figure out a band where wheel spin actually moves the car forward and above that range have the car slip right more than usual. In the Dirt Track Racing games which do drift very well, to high a wheel speed does not grip the track enough to allow any forward bite (or acceleration). Find the range where you want forward bite should allow you to figure out how you want to handle drift.
I know that there is no code or examples to work with but instead a discussion of the effect. I think you are a better programmer than I so you can code something that you can tweak and decide the formula that suits your needs.
Good luck.
Wasting CPU Cycles since the 286 was a hot machine.