Go kart cvt?

66cc is too small of an engine. A CVT taxes power due to frictional losses.
66'rs don't make alot of power to begin with (less than 3hp) and the power lost in the CVT will be a substantial portion of what could have gone to the rear wheel.
Alot of folks have tried CVT's on the 4 stroke HF 99cc engines with marginal success, most don't like it. The most popular engine to use with a CVT is the 4 stroke HF 212cc.

I gotta ask though, which 66cc engine do you have in mind? A well built 2 stroke might just have enough cajones to pull it off, although you would need to customize the CVT to work with the higher RPM's that a 2 stroke operates at.

how do you plan on mounting this to a 66cc smoker, since im going out on a limb and assuming your talking about a 66cc china doll kit engine. if this is the case, be warned, you probably wont be able to drive it off of the out put sprocket because of the 4.2:1 primary reduction. if you want a two stroke and a cvt, why not hunt around for a CAG motor with a CVT on it, they are around, kinda hard to find, but they are out there