Virtually impossible. It can definitely be done, but at the end of the day, you probably would have been better off buying a complete bike with all of the corners you would have to cut on components.

I'm pretty sure there are a handful of threads on finding a good quality, low priced complete fixed gear (bikes direct comes to mind), but I'm going to agree with the others and say your current frame is a lost cause. I'm about 5'8" and have a hard time with 56cm bikes so I have absolutely no idea how you're riding a 61cm. Im assuming it's not comfortable at all and an overall challenge to ride.