Yep.
Just use the old trans axle from it. Most stock garden tractor trans-axles are rated for about 5 - 10 actual driven HP with a 800 - 1200 RPM input. But thats with the high reduction in place from the belt drive system.
Buy changing it from a speed reduction to a speed increase you can get up to around 8 - 10 times the ground speed out of one with out any problems.

One thing you would probably need to do to increase the longevity of the trans axle is to take it apart and replace the old thick grease with a synthetic grease and gear oil mix for added lubrication when running with the much higher speeds.

A larger capacity centrifugal clutch that has had its its chain drive sprocket machined off so that a larger belt pulley can be welded on is about all it takes to set it up for a sort of automatic clutch system.

If you went with a 2:1 speed increase over the old stock reduction of around 3:1 - 4:1 you likely could see a 20 - 30 Mph top end in high gear.

One down side is the old disk break system on most trans-axles dont take the high speed stops so well. The stock disks are typically too small. If a hydraulic caliper system from an old motor cycle and bigger disk was refitted to it it would not be a problem.

I built my nieces go cart this way and it has not had any drive train problems so far.
The 5 forward speeds and reverse plus the full dual rear wheel drive are much nicer to drive than the old one wheel one speed wonder most go carts use.

Sorry if this is off topic, but when gabeNC mentioned "mechanical/redneck engineering", I couldn't resist sharing my all-time favorite

http://www.youtube.com/watch?v=gd49-yuFNDc

Some technical details

YouTube - how to build the redneck rollercoaster

My friend and I built a Mow-Kart awhile back. Didnt take much modifications. We put a small pulley on the motor and one that had an adjustable diameter on the tranny. We were able to set it so we had decent power through the 3 gears. Also rigged up a throttle pedal and modified the clutch/brake pedal so it was just a clutch.
Boy that was alot of fun. We also put a straight pipe on the exhaust. It sounded real mean.

I would watch out on the removing the governor though. Very few small engines will take being over reved all that far past their typical 3600 RPM rating. They tend to shatter the stock connecting rods rather easily if they get up much faster than their stock rating.

Ive seen and done it a few times myself!